Imagery in Winter’s Tale

†¦Ã¢â‚¬ ¦. It is time for Polixenes, King of Bohemia, to end his visit with his boyhood friend Leontes, King of Sicily. While the two kings prepare to bid farewell in a state room of the Sicilian palace, a Bohemian lord named Archidamus and a Sicilian lord named Camillo are in an antechamber discussing the extraordinary friendship between the two rulers. Camillo, advisor to Leontes, observes that they were inseparable when growing up: â€Å"They were trained together in their childhoods; and there rooted betwixt them then such an affection, which cannot choose but branch now† (1. . 10). †¦Ã¢â‚¬ ¦. Archidamus says nothing will ever come between the two kings. (His observation is an ironic foreshadowing of a terrible jealousy that will soon divide them. ) He also praises the Sicilian king’s little boy, Mamillius, as the finest of lads with the brightest of futures. (This, too, is an ominous observation. ) †¦Ã¢â‚¬ ¦. In the state room, King Leontes presses K ing Polixenes to linger in Sicily one more week, but Polixenes begs off, worrying about â€Å"what may chance / Or breed† (1. 2. 15-16) in Bohemia in his absence. When Hermione, the beautiful wife of Leontes, joins her husband in importuning Polixenes to extend his visit, he agrees to remain a while longer. Pulling him aside, she asks what his childhood was like with her husband. Polixenes replies, We were, fair queen, Two lads that thought there was no more behind But such a day to-morrow as to-day, And to be boy eternal. (1. 2. 78-81) When Hermione asks about their childhood adventures, Polixenes says, We were as twinn’d lambs that did frisk i’ the sun, And bleat the one at the other: what we chang’d Was innocence for innocence; we knew not The doctrine of ill-doing, nor dream’d That any did . . . . (1. 2. 83-87) After Leontes learns that Hermione has persuaded Polixenes to stay, Leontes immediately regrets extending Polixenes’s welcome, for the friendly conversation between his wife and Polixenes has envenomed him with jealousy. Apparently, Polixenes has an unduly suspicious eye. Perhaps Polixenes and his wife have become too close, Leontes thinks; perhaps they have been meeting in secret. He even begins to wonder whether his son, Mamillius, is the the product of a tryst in an earlier time between Hermione and Polixenes. †¦Ã¢â‚¬ ¦ Later, suspicion builds upon suspicion. In a conversation with Camillo, the king openly accuses his wife of infidelity. Camillo, shocked, says the king sins gravely in speaking against her. The king replies, Is whispering nothing? Is leaning cheek to cheek? is meeting noses? Kissing with inside lip? stopping the career Of laughing with a sigh? (1. 2. 332-335) †¦Ã¢â‚¬ ¦ . Finally, he orders Camillo to bear a poisoned cup to Polixenes. Camillo tells the king he will perform the deadly mission, but then warns the Bohemian king that his life is in danger. During the night, Polixenes steals away. Camillo, estranged by Leontes’s behavior, accompanies Polixenes. Their sudden departure convinces Leontes his suspicions against Hermione are well founded. Angry and bitter, he publicly denounces his wife, who is soon to have another child, as an adulteress. After imprisoning her, he deprives her of the company of little Mamillius. Hermione pleads her innocence, to no avail. She is guilty; Leontes is certain of it. To confirm her guilt for others, he sends two lords, Cleontes and Dion, to the Oracle at Delphi, Greece, to request a judgment. †¦Ã¢â‚¬ ¦ After Hermione bears a daughter, her servant, Paulina, presents the infant to Leontes, hoping the sight of the little girl will quench his anger. However, wrathful as ever, Leontes disowns the child–believing it is not his own–and orders Paulina’s husband, Antigonus, to abandon it in a far-off place. Leontes then subjects Hermione to a public trial. With utmost dig nity and grace, she proclaims her innocence, declaring she has always been faithful to Leontes. †¦Ã¢â‚¬ ¦. During the trial, Cleontes and Dion return from Delphi with a sealed verdict from the great Oracle. An official of the court breaks the seal and reads the verdict: â€Å"Hermione is chaste; Polixenes blameless; Camillo a true subject; Leontes a jealous tyrant; his innocent babe truly begotten; and the king shall live without an heir, if that which is lost be not found† (3. 2. 134). †¦Ã¢â‚¬ ¦. Leontes rejects the verdict and orders the trial to continue. A servant interrupts the proceedings with tragic news: Prince Mamillius, pining for his jailed mother’s love, has died. The news staggers Leontes, and Hermione collapses. Suddenly realizing how wrong he as been, Leontes tells Hermione’s attendants to treat her gently when they escort her from the courtroom. Later, Leontes receives another shock: Hermione, too, has died. Profoundly moved, the king laments his vengeful deeds and goes off to mourn. †¦Ã¢â‚¬ ¦. What of the newly born child, the infant princess? As instructed, Antigonus leaves her in a far-off place, the coast of Bohemia, along with certain effects, including a note identifying the infant as â€Å"Perdita,† a name that came to Antigonus when he imagined he saw Hermione in a vision. But before Antigonus can return to his ship, a bear attacks and kills him and an angry sea wrecks the ship and swallows it and all aboard. Consequently, no one is left to report the fate of the child. A clown, the son of a 67-year-old shepherd, witnessed the bear attack and gives a report to his father, who discloses news of his own: He has found a baby girl on the coast along with a â€Å"bearing cloth† and gold. Sixteen Years Pass †¦Ã¢â‚¬ ¦. Shakespeare updates the audience on important developments through a speaker called Time. He tells the audience that Leontes now lives in seclusion and that the setting of the drama has shifted to Bohemia, where the son of Polixenes has fallen in love with a shepherdess. †¦Ã¢â‚¬ ¦. In Bohemia, Polixenes stews about his son, Florizel, because the young man frequently visits the house of an elderly shepherd to woo his beautiful sixteen-year-old daughter, Perdita. Because of her lowly status, she is unworthy of Florizel’s attentions, Polixenes believes. †¦Ã¢â‚¬ ¦. Polixenes and Camillo, who has become the advisor of the king, decide to call at the shepherd’s house to observe Florizel and Perdita during a sheep-shearing and feast in which visitors are welcome. They wear disguises. Also present are the old shepherd and his son; a shepherdess, Mopsa (who hopes to marry the shepherd’s son) and her friend, Dorcas; and a thief, Autolycus, who has presented himself as a seller of ballads after arriving while singing a song. Earlier, Autolycus had picked the clown’s pocket on a road near the shepherd’s cottage. †¦Ã¢â‚¬ ¦. When Polixenes discovers that Florizel plans to marry Perdita, Polixenes reveals his identity and threatens retaliation against anyone who abets the wedding plans. Sympathizing with the lovers, Camillo persuades them to abscond to Sicily. Later, at Camillo’s request, Autolycus assists in the escape plan by gladly trading his shabby clothes with the princely garb of Florizel. Dressed as a commoner, Florizel will be able to avoid detection on his way to a ship. Before returning to the palace, Camillo tells the audience in an aside that he will provoke Polixenes into following the lovers. His purpose is not to betray the lovers; rather, it is to go with Polixenes to Sicily, for which Camillo has been homesick these many long years in Bohemia. His scheme works and Polixenes prepares to follow the lovers in his own ship. †¦Ã¢â‚¬ ¦. Elsewhere, the old shepherd and his son are on their way to see Polixenes at his palace. The shepherd carries a box containing keepsakes of Perdita from long ago. These objects, he believes, will prove that Perdita is not his daughter and, thus, enable him and his son to escape the king’s wrath. On their way, they meet Autylocus, still dressed in Florizel’s clothes; they think he is a royal personage. When he says the king is about to embark on a ship to chase Florizel and Perdita, they offer him gold to take him to the ship and speak for them. But because he is not who he says he is, he takes them to Prince Florizel’s ship. All of them–Florizel, Perdita, Autolycus, the old shepherd, and his son–then set sail for Sicily ahead of the king’s ship. Many days pass while the ships are at sea. The setting then shifts to Sicily. †¦Ã¢â‚¬ ¦. When Florizel and Perdita arrive at the palace of Leontes and wait for an audience with him, a gentleman of the court informs the king of their presence, announcing them as the Prince and Princess of Bohemia. He says the princess is the most beautiful creature he has ever seen. †¦Ã¢â‚¬ ¦. After they are escorted into the court, Florizel greets Leontes on behalf of his father, Polixenes, saying an infirmity prevented Polixenes from making the trip himself. When Leontes inquires about the lovely Perdita, Florizel describes her as the daughter of a Libyan lord. He and the princess sojourned in that African country, he says, before sailing to Sicily to carry out a mission for his father. While Leontes visits with the young couple, all of the others from Bohemia assemble at the court: the old shepherd, his son, and Autolycus, as well as the travelers from the other ship–King Polixenes and Camillo. †¦Ã¢â‚¬ ¦. Leontes, now a reformed man who is deeply sorry for his past misdeeds, reconciles with Polixenes and Camillo. The old shepherd and his son then reveal the contents of the mysterious box of keepsakes. It contains a â€Å"bearing-cloth† (3. . 77) Hermione had given to Antigonus. Leontes recognizes it as Hermione’s, unique because of a jewel on it. He also recognizes the handwriting in the note Antigonus left before a bear attacked and killed him. Just as convincing as these items identifying Perdita is the remarkable resemblance Perdita bears to Hermione. King Leontes joyfully reunites with his daughter and accepts Florizel as his future son-in-law; Polixenes accepts Perdita as his future daughter-in-law. †¦Ã¢â‚¬ ¦. Leontes’s joy, though, is tinged with sadness, for he still grieves over the loss of Hermione. Paulina, the servant who sixteen years before pleaded on Hermione’s behalf, then invites Leontes to her house to show him a statue of Hermione, sculpted by an Italian master. While the royals and nobles are on their way to Paulina’s, Autolycus begs and receives the forgiveness of the old shepherd and his son for deceiving them back in Bohemia, then taking their gold and putting them on the wrong ship. †¦Ã¢â‚¬ ¦. Upon viewing the statue at Paulina’s house, Leontes discovers that it is no statue; it is the real Hermione. She has been living in hiding with Paulina these many years praying for the return of her daughter. Paulina was afraid to disclose Hermione’s whereabouts for fear of interfering with the will of the Delphic Oracle, as expressed in the prediction that â€Å"the king shall live without an heir, if that which is lost be not found† (3. 2. 134). In other words, Leontes–if reunited earlier with Hermione–might have fathered another child. In so doing, he would have produced an heir before his lost child had been found. The will of the Oracle would have been defeated. When Perdita appears, Hermione rejoices and invokes the gods to bless her child. The joy of the occasion spills over to include a proposal by Leontes that Camillo and Paulina marry. †¦Ã¢â‚¬ ¦. And what of Mamillius, the little prince? Nothing can bring him back, but Leontes does have a new son in the person of Florizel. . Now Available†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ Shakespeare: a Guide to the Complete Works†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. In Hardback & Paperback By the Author of This Web Site . Plot Summaries of All the Plays and Narrative Poems | Themes | Imagery | Historical Background | Glossaries Shakespeare's Theatre | Drama Terms | Essays | Analysis of the Sonnets | and Much More .. . Characters . Protagonist: King Leontes Antagonist: The King's Jealousy and Suspicious Nature . Leontes: King of Sicilia (Sicily). He is a headstrong man who is at first guided more by emotions than reason. His unfounded suspicions against his wife, Hermione, and his friend, King Polixenes, separate him from both of them and cause him to reject his infant daughter. His unjust actions also indirectly result in the death of his son, Mamillius. In many ways, he resembles the flawed protagonists of Greek tragedy; however, reforms himself before it is too late. Hermione: Honorable and loyal Queen of Sicilia. Polixenes: King of Bohemia. He opposes his son's marriage to Perdita, believing her to be a commoner. Although he accepts Perdita at the end of the play, he does so only after he learns her true identity. Whether he has overcome his prejudice against commoners remains open to question. Perdita: Extraordinarily beautiful daughter of Leontes and Hermione. Florizel: Prince of Bohemia. Mamillius: Young prince of Sicilia. His death adds a tragic element to the play. Camillo: Upright advisor of King Leontes. After Leontes order him to poison Polixenes, Camillo returns with Polixenes to Bohemia and becomes his advisor. Old Shepherd: Reputed father of Perdita. He is 67 when the infant Perdita is found and 83 at the end of the play. Clown: The shepherd's son. Autolycus: A comic thief and pedlar who assists Florizel and Perdita. Gaoler (Jailer) Paulina: Loyal attendant of Hermione. Antigonus: Kindly husband of Paulina. He rescues the infant Perdita and takes her to Bohemia. Cleomenes, Dion: Lords of Sicilia. Archidamus: A Lord of Bohemia. Mariner: Crewman of the ship that carries Antigonus and Perdita to Bohemia. Emilia: Lady attending Hermione. Mopsa, Dorcas: Shepherdesses. Rogero: Lord who tells other gentlemen that a prophecy by the Delphic Oracle has been fulfilled. Minor Characters: Other lords, gentlemen, ladies, officers, servants, shepherds, shepherdesses. . Settings . The action takes place in Sicily (or Sicilia) and Bohemia. Sicily is a large island west of the toe of Italy's boot. Bohemia was a kingdom within the boundaries of the present-day Czech republic, between present-day Poland on the north and Austria on the south. In ancient times, a Celtic people called the Boii settled the land that became Bohemia. In The Winter's Tale, Bohemia has a coastline along which ships arrive and debark. In real life, Bohemia was a landlocked region; it was entirely surrounded by terra firma. Shakespeare may have been a magnificent writer, but he was no geographer. .. Climax . The climax of a play or another narrative work, such as a short story or a novel, can be defined as (1) the turning point at which the conflict begins to resolve itself for better or worse, or as (2) the final and most exciting event in a series of events. The climax of The Winter's Tale occurs, according to the first definition, when Leontes receives news of the death of his wife and son, then owns up to the grave sin he has committed in doubting the fidelity of his wife. According to the second definition, the climax occurs in the final act when Leontes reunites with his daughter, whom he abandoned when she was an infant, and with his wife, whom he thought was dead.

Implications of Day Care in Young Children Essay

Within this assignment I will be discussing the implications of day care for young children and giving both the positive and the negative aspects of this. A study was done in the united states by Kagen (1978), the study was done on children whose mothers worked, in which case the children were put into day care centres compared to home –reared children. Kagen found little difference between the children placed in day care centres and those raised at home either in the amount of protest or seeking closeness to their mothers when upset. From the findings it appears that it doesn’t matter if a child is in day-care or raised at home or the amount of hours spent with its mothers, there is a special bond between mother and child. Bee (1974) Concluded that there are no negative effects when a child is cared for in a day care centre, provided these are run by trained professionals and only a small number of children. However, Bee (1997) also suggests â€Å"The crucial issue is the discrepancy between the level of stimulation that the child would receive at home and the quality of day care. When the day care setting for the child provides more enrichment than the child would normally receive at home, we see some beneficial cognitive effects. When day care is less stimulating than the child’s home care would have been, it has negative effects.† Psychologists disagree about the developmental effects of day care on young children. Some agree with Bowlby’s prediction that long to medium term separation from the mother could have far-reaching consequences. Others claim that, provided day care is high quality day care has no adverse effects on intellectual development and does not disrupt the child’s attachments. Some psychologists believe that it might even make a positive contribution to the child’s development. The type and quality of care can influence many aspects of development—including memory, language development, school readiness, math and reading achievement, the nature of relationships with parents and teachers, social skills, work habits, and behavioural adjustments Below I have tried to outline the positive and negative aspects of day care: – Positives * When children attend nursery or playschool it’s clear that peer relationships take on increasing importance but peer relationship importance  is important before this . Early as 6 months old babies smile and are more vocal to other infants. * Intellectual stimulation * Helps develop some social skills- building relationship with peers and other trusted adults other than those within the family. * Psychologists have shown there is no affect on the mother-child attachment * Children receive Adequate and nutritious meals Negatives * Putting a child into day care can cause the child stress ( i.e upset from being away from its mother)as can any situation in which the mother isn’t with the child. * If a day care doesn’t have the correct form of attachment for adults and the children as mentioned above ( conclusion raised by Barbara Tizard) this will not have as greater benefits as a quality day care that has this attachment and familiarity etc. * Some research in the US argue that day care can cause the child to grow up to be aggressive and disruptive once they reach school age (research taken from -NICHD national child care study)

Four Styles of Creative Intelligence Essay Example | Topics and Well Written Essays - 750 words

Four Styles of Creative Intelligence - Essay Example The four styles of creative intelligence are as follows, first is Intuitive, this is based upon the past experience and it is one of the most widely trusted styles of creative intelligence. The biggest advantage of this style is that the past experience is taken into consideration when adopting this method, when past experience is considered many new things can be learnt from the same as experience is believed to be the best teacher. Many mistakes can be avoided making the most of this method; hence it is a very good style to follow as far as creative intelligence is concerned. Second style is Innovative; this is another highly adopted style. Organizations come across new problems everyday and in order to solve the problem one needs to come up with new solutions and what Innovation is all about. Innovation focuses upon new methods to tackle problems, every organizations looks for this quality in its employees. Innovation is based upon a systematic approach to problems and it's all about coming up with solutions to the problem. This is another very highly adopted style of creative intelligence which is used by more organizations than one these days. The third style of creative intelligence is Imaginative. ... There is no certainty whether their ideas would prove beneficial to the organization or not. On the contrary if the ideas click then the organization would surely find itself sitting in a very comfortable position. So it is like a gamble which might pay off or it might not pay off. The last style of creative intelligence is Inspirational; this is more like motivation where the employees are inspired and motivated to achieve the goals of the organization. Every organization should follow this style in order to make sure that all the employees work towards the same goals set by the organizations. Using this style has many advantages; the biggest of them all is that the employees start working selflessly and ultimately the growth of the organization as well as the employees take place. So it is advisable to use this style of creative intelligence to make sure that the employees try and meet all the goals set by the organization. The five forces that influence the mind set and hence go on to influence the decision making procedure are as follows; First is the entry of competitors, this brings a lot of worries to an organization. The organizations starts considering various factors like "What are the Absolute cost advantages Which barriers do exist How easy or difficult is it for new entrants to start competing" (Porters Five forces model, 13 October 2008). It is very essential to do an in-depth analysis on the competitors in the market to know where the organization relay stands, hence this step becomes inevitable. The next is Threat of Substitutes, things like "How easy can a product or service be substituted Can products be made cheaper What are the switching costs" (Porters Five forces model, 13 October 2008) come

Geography home work Essay Example | Topics and Well Written Essays - 500 words

Geography home work - Essay Example Social media took five years to be accepted and be the most used means of communication and lifestyle by college students replacing mainstream means of accessing information, communication, and interaction. 3. I adopted the use of social media very early in the S-curve owing to the widespread of its use and that it was a new innovation while I was a late adopter on the use of computers in social networking and communication owing to low financial liquidity. 5. The diffusion of AIDS in the United States follows an S-Curve diffusion pattern as reflected in the changes in the rates of prevalence according to region and the reduction in new infections in recent years. 6. The main reason for New York, Miami, and LA/SF were the high rates of drug abuse that allowed the use of and sharing of needles, social status and sexual habits that promoted having unprotected sex and high population density as they are urban regions and it was the main areas where AIDS began then spread. 12. The characteristics that determine if a phenomenon will diffuse hierarchically of contagiously include the mode of contamination for example direct contact for a disease or means of transfer of ran innovation, the source of the phenomenon and the ability to be transferred through relocation or migration to new areas. 14. I would apply my knowledge of spatial diffusion through development of products for different age brackets that will be transferred through relocation and expansion diffusion when one has the product or listens to the music through correspondence and migration to different areas with them. There are several instances where the Middle East and the American Southwest have differed especially on policies on terrorism, religion, and democracy. Muslim oppression, independence, and traditional cultures being impended by globalization of western culture are some of the reasons for the bombing of World Trade Center and Pentagon by Muslim terrorists. Despite these

Gibbs Paradox Essay Example | Topics and Well Written Essays - 1500 words

Gibbs Paradox - Essay Example : For a solid structure of perfect symmetry (e.g., a perfect crystal), the information I is zero and the (information theory) entropy S is at the maximum. If entropy change is information loss, ?S = I , the conservation of L can be very easily satisfied, ?L = ?S + ?I = 0 . Another form of the second law of information theory is: the entropy S of the universe tends toward a maximum. The second law given here can be taken as a more general expression of the Curie-Rosen symmetry principle [5,6]. The third law given here in the context of information theory is a reflection of the fact that symmetric solid structures are the most stable ones. Indistinguishable Particles:- Two particles are called identical if the values of all their inner attributes agree. H must be so constituted that the transposition of two identical particles is defined for every vector in H (quantum case) or every phase space point in H (classical case), respectively. Two identical particles are called indistinguisha ble if every pure quantum state (every classical microstate) is invariant under transposition of these two particles; otherwise the two particles are called distinguishable. Two non-identical particles are always considered distinguishable. Resolution of the paradox in terms of Indistinguishable particles:- In the preceding section as I discussed about indistinguishable particles (Two particles are said to be indistinguishable if they are either non-identical, that is, if they have different properties, or if they are identical and there are microstates which change under transposition of the two particles.) The GP1 is demonstrated and subsequently analyzed. The analysis shows that, for (quantum or classical) systems of distinguishable particles, it is generally uncertain of which... The GP1 is demonstrated and subsequently analyzed. The analysis shows that, for (quantum or classical) systems of distinguishable particles, it is generally uncertain of which particles they consist. The neglect of this uncertainty is the root of the GP1. For the statistical description of a system of distinguishable particles, an underlying set of particles, containing all particles that in principle qualify for being part of the system, is assumed to be known. Of which elements of this underlying particle set the system is composed differs from microstate to microstate. Thus, the system is described by an ensemble of possible particle compositions. The uncertainty about the particle composition contributes to the entropy of the system. Systems for which all possible particle compositions are equiprobable will be called harmonic. Classical systems of distinguishable identical particles are harmonic as a matter of principle; quantum or classical systems of non-identical particles are not necessarily harmonic, since for them the composition probabilities depend individually on the preparation of the system.

Marketing Strategy of Aer Lingus Assignment Example | Topics and Well Written Essays - 5000 words

Marketing Strategy of Aer Lingus - Assignment Example Currently, Irish government holds 25.1% of shareholding in Aer Lingus. The airline company operates as ‘value carrier’ while it has signed number of agreements air line companies of other countries such as Aer Arann, Air Bus etc in order to manage its low cost services. Primary market for Aer Lingus includes Republic of Ireland, continental Europe, UK and USA. In the year 2012, the Irish airline company has carried more than 9.6 million passengers across the boundaries. In the year ended 31 December 2012, the company has reported annual revenue of more than â‚ ¬1,350 million with operating profit hovering over â‚ ¬65 million. The company has established its base airport in Belfast City and shown the interest to expand its destination routes by 2 times in next couple of years (Competition Commission, 2013). The Irish airline carrier has established its base in Belfast City along destination points include Manchester, Birmingham, Gatwick and Heathrow airports of UK ( Competition Commission, 2013). Great Britain-Ireland destination root contributes 30% to 33% of the top line growth and 45% of total passengers for Air Lingus. Until 2001, Aer Lingus operated as full service carrier but after 9/11 world trade centre terrorism the company has transformed itself as low-cost carrier. Since 2009, the company has completely changed its positioning statement has become ‘value carrier’ by serving centrally located airports in order to decrease its travel path and save the fuel cost in order to deliver service to customers at competitive price. The company has also entered in partnership with existing low-cost airlines in order to deliver low cost services to customers...Conjoint impact of reduction of disposable income of consumers and entry of resource rich international airlines have pushed Aer Lingus to reposition as value carrier. Hence it can be said that, although the problem for Aer Lingus is strategic in nature but the brand can reposi tion itself with the help of integrated marketing communication strategy. However, let’s try to understand changing macro environmental challenges for Aer Lingus in terms of PESTLE Analysis. VCCP Blue (2008) has pointed out that Aer Lingus spends only â‚ ¬2 million for implementing its IMC plan which is way below than the industry average of advertising to sales ratio (A/S ratio). Hence it is recommended for the company to increase its advertising position in order to use all channels of communication in effective manner. On the basis of PESTLE analysis, it can be said that the company needs to promote its green initiatives such decreasing the carbon emission in short haul travel, creating greenery in African nations etc in the form of press release. They need to use the print media advertisement in order to release key benefits that can be achieved through merger & acquisition in order to create positive word of mouth regarding the event among customers. Such kind of indirect lobbying also help Aer Lingus in legal proceedings.

Data Collection and Analysis Essay Example | Topics and Well Written Essays - 1000 words

Data Collection and Analysis - Essay Example Depending on the need, availability of information and expected outputs one or combination of more than one methods for data collection and analysis needs to be adopted. Following are some of the methods for data collection - 1. Primary Research - this method involves collecting information from first hand research done by other individuals / teams / groups and using it to draw inferences with due references to the original research work. 2. Secondary Research - this method involves collecting information which has been derived or inferred from some other primary research work. This may involve articles, secondary research reports, published opinions, etc. among others. 3. Survey - this is a widely known method of data collection by conducting a survey over a sample target population and analyzing the results in order to get first hand information on the research work. 5. Interviews - interviews are another form of collecting information from relevant target population and use the information captured to satisfy the research objectives. Interviews can be structured or unstructured and can be conducted in person or on phone or video conference. 6. Delphi Method - this is a method for collection of expert opinion in the area in which research is being conducted. Experts consulted should be credible and knowledgeable people in the area of the research. For each of the data collection met... However, the above list captures the most commonly used data collection methods. Pros and Cons For each of the data collection methods stated above, there are pros and cons of adopting them in a research project as well as appropriateness for specific type of research projects. Following is a brief discussion on the same - 1. Primary Research - this is a good method of data collection as it provides valuable data points for the research without actually conducting a firsthand research. This method is useful where there are constraints on either time or resources for conducting fully fledged research activities. However, this is still a substitute for actual research. Information available may not exactly match the conditions needed for the research. Hence, there may be compromises or assumptions to be made while using this form of research. This may lead to inaccuracies in research results. 2. Secondary Research - similar to primary research, secondary research may also used in cases of constraints on resources or time. Many times, this form of research is used as a literature review for first step in a research project to provide rough idea on the research topic. This provides important data points which may be useful for designing the actual research, tools used and analysis of data. Again, the disadvantages are that the secondary source information may have inherent inaccuracies introduced while drawing inferences and conclusions from the primary research sources. 3. Survey - this is a popular data collection tool used while conducting business research or market research. The survey results and their analysis provide first hand information directly from the main sources and are not dependent on inferences or

The effect of immigration on US economy Essay Example | Topics and Well Written Essays - 1250 words

The effect of immigration on US economy - Essay Example This decrease was a result of reduced job opportunities and increased law enforcement. (Giovanni 24) Despite this reduction, researchers found that the reproduction could have contributed the reduction of immigrants. A good number of immigrants have children, who are recognized legally as US citizens, others intermarried gaining their citizenship by marriage. Although it is hard to estimate the actual number of immigrants living in the US, researchers estimated that a third of the total population living in the US is illegal. Recent reports released by the center for immigration studies showed that in the year 2012, 12 million immigrants arrived in the United States temporally using non-immigrants visas. This figure translates to a 50% total population by the year 2000. Significant number of these illegal immigrants was from Mexico. For over a decade, there has been rapid distribution of immigrants in the United States. Georgia reported the immigrant population growth rate of 152% between year 2000 and 2007. California grew by 10.2%, registering the largest number of immigrants in the United States. Consequently, California can comfortably offset its fiscal cost. Although this immigration may be caused by historical and geographical factors, economic growth is achieved. For instance, if a state is experiencing rapid growth in terms of economic conditions, it might end up encouraging immigrants and affect income, output and employment. Analysis by various physiologists says that, reasonable arguments are being raised to protect all American-born workers from competition from immigrants. The United States government is enforcing strict laws to prioritize recognition of American born citizen (Nwosu, Batalova and Auclair 56). Immigrants are allowed to keep transportation, natural resources, construction and maintenance occupation and material moving occupations. On the other hand, the

Financial Market Essay Example | Topics and Well Written Essays - 500 words

Financial Market - Essay Example The value of the Euro to the dollar has shown the success in gaining value over the US dollar. In January 2009 the exchange rate was 1Euro/USD 1.3866, in January 2010; the rate changed to 1Euro/USD 1.4389. This upward trend shows that the Euro is getting stronger in the forex market as compared to the US dollar. In 2012, the value of exchange dropped to 1Euro/USD 1.2458. Despite this drop, the value of the Euro is still higher than that of the US dollar. The Japanese Yen is the domestic currency used in Japan. The Yen has developed a relative stability and its recent reputation has led to investors opting to use this currency as a secure investment for the dollar. In 2001 the exchange rate was 1$/Yen 121.2, in the year 2005, the Japanese Yen gained against the US dollar in the forex market where the exchange was 1$/Yen110.2. The trend continued where the Yen continued gaining against the US dollar. Even though today’s exchange rate for the Yen to the dollar is still high at 1$/Yen79.8 the Yen has shown its success by increasing its value and minimizing the spread (Euromonitor International). The Canadian dollar is also gaining popularity among the investors across various parts of the world. As part of its success, its increasing use in the forex markets has shown that investors have recognized its stability. This currency has a remarkable use in transactions and enjoys over 4% of all transactions in the foreign exchange market daily. This is remarkable success in the forex market for this currency. For instance, the exchange rate for the Canadian dollar in 2001 was 1$/CAD1.5 while in 2005, the exchange rate changed to 1USD/CAD1.2; while in 2012, the exchange rate is 1USD/CAD1.0. This shows that the Canadian dollar gained strength against the US dollar to exchange thus it can be termed as a success to the Canadian dollar at the expense of the US dollar. The Swedish dollar is the Sweden’s currency. Its transactional use is above

Single Parent Households and Crime Essay Example for Free

Single Parent Households and Crime Essay People claimed that growing up in a fatherless or motherless home was the major cause of child poverty, delinquency, and school failure, while others denied that single parenthood had any harmful effects. And some objected even to discussing the topic for fear of stigmatizing single mothers or fathers and their children. Not talking about single parenthood is scarcely an option. More than half of the children born in 1994 will spend some or all of their childhood with only one parent, typically their mother. If current patterns hold, they will likely experience higher rates of poverty, school failure, and other problems as they grow up. The long-range consequences could have enormous implications. (Article/consequences-single-motherhood familyinequality.wordpress) But what exactly are the consequences how large and concentrated among what groups? Do they depend on whether a single mother is widowed, divorced, or never married? Does public support for single mothers inadvertently increase the number of women who get divorced or choose to have a baby on their own? Children who grow up with only one of their biological parents (nearly always the mother) are disadvantaged across a broad array of outcomes. They are twice as likely to drop out of high school, 2.5 times as likely to become teen mothers, and 1.4 times as likely to be idle out of school and out of work as children who grow up with both parents. Children in one-parent families also have lower grade point averages, lower college aspirations, and poorer attendance records. As adults, they have higher rates of divorce. These patterns persist even after adjusting for differences in race, parents education, number of siblings, and residential location. (Article/consequences-single-motherhood familyinequality.wordpress) The evidence, however, does not show that family disruption is the principal cause of high school failure, poverty, and delinquency. While 19 percent of all children drop out of high school, the dropout rate for children in two-parent families is 13 percent. Thus, the dropout rate would be only 33 percent lower if all families had two parents and the children currently living with a single parent had the same dropout rates as children living with two parents a highly improbable assumption. (Article/consequences-single-motherhood familyinequality.wordpress ) Family disruption also undermines childrens access to community resources or what sociologist James Coleman calls social capital. Divorce and remarriage often precipitate moves out of a community, disrupting childrens relationships with peers, teachers, and other adults. During middle childhood and early adolescence, a child in a stable family experiences, on average, 1.4 moves. The average child in a single-parent family experiences 2.7 moves; in a stepfamily, the average child experiences 3.4 moves. (ejournal.narotama.ac.id/files/DeMuthandBrownJRCD) So all this information provided, I agree that children growing in a single parent household, and a child having family disruptions, does impact delinquency within in juveniles I’m not saying it’s a 100% guarantee a child will fall into delinquency because of one parent households, I’m just agreeing that the possibility is a higher risk.

Marketing, Communications and Fundraising of NGO

Marketing, Communications and Fundraising of NGO Chikondi Mbewe Introduction Urban Promise Wilmington is a Christian organization focusing on serving at-risk children and youths in Delaware State. It was founded in 1998 by Rob Prestowitz. The vision of the organization came into existence when the founder volunteered in Camden. The city of Wilmington is still known as one of the most unsafe cities in America due to violence and drug abuse. The violence and drug abuse does not only affect the communities but also in the lives of young people who have a future. Urban Promise is raising a generation of hope of Christian leaders on the East side of Wilmington where there are shootings going on observed Miller, (dalawareonline.com Sunday News Journal A17, 2010). In 1999, the organization started running afterschool program, targeting elementary children at St Joseph Catholic Church. From 2001, the organization extended its program to some three new sites: Camp Promise, Camp Freedom, Camp Hope, and own an elementary school. Other two middle school Camps were also o pened to reach out at-risk youths. In 2010, the organization embarked on another big project of opening urban Promise Academy high school. The Mission Statement The mission of Urban Promise is to equip children and young adults with the skills necessary for spiritual growth, academic achievement, life management and Christiana leadership. The vision is to be a community in Christ of transformational and servant leadership, seeking a full life for all involved, urban youths and families, volunteers and staff in the neighborhood our city Wilmington. Market Mix Marketing mix refers to a unique blend of product, place (distribution), promotion, and pricing strategies designed to produce mutually satisfying exchanges with a target market (Lamb, 2009 p.47). Product, place, promotion and price are the major elements that determine the market. How does the product affect the market or the needs of the customers? Product Products refer to tangible goods, series, places, and ideas which customers buy, lease, rent, or use to meet their needs and wants (Wood, 2011 p. 97). Any company or nonprofit organization before it goes on the market, there are a number of questions needs to be answered. What are we really selling? What are the features of our product or services? What are the benefits of our products or services to the customers? Who is our target audience primary, secondary or tertiary? As an organization, answering such questions can help to be focused on what it wants to deliver to the customer needs with quality and satisfaction. Urban Promise Wilmington does not produce tangible goods but rather services As such our services are programs that we offer such as Afterschool program in six sites, Urban Promise Elementary school program, Urban Promise High school Academy, Summer Camp, Trekkers Program, Street Leader job Training program, and Intern Program. The features of our services are the quality of the programs offers to the communities, children, and youths that are Christ centered. The benefits of our services look beyond current challenges to see a future of hope and purpose. Such benefits include educational performance, spiritual enhancement, life skills management and behavior change management for young people. The programs enrich kids in a safe, positive environment during high-risk hours. More personalized assessment and focused intervention. Motivational programs such as speech contest, spelling and math bees, college trips, UK speaking tour as we train the minds and disciple the hearts. Price Price is that which is given up in an exchange to acquire a good or service (Lamb, 2009 p. 559). Price can easily determine the value of the product or vice-versa. if customers perceive the price to be too high in relation to the benefits, they simply wont buy, which helps to lower demand; if they perceive the price to be too low, for the expected benefits or quality, demand also will suffer (Wood, 2011 p. 115). This suggests that the price is the deciding factor to create more demand for the service or supply. But in most cases, customers focus on the benefits of the service or product. Time also affect price especially in times of low inflation, business can increase profit margins only by increasing efficiency (Lamb, p 86 bright space article chapter 3) In this case, Urban Promise Wilmington, it offers free Afterschool program but there is still an element of price for some services. The free Afterschool program is one of the strategies to achieve its mission and against competitors. For example, College trips, children, and youths pay $10, summer camp each kid pay $25 which is used to buy summer T-shirt, and the field trip every Friday for six weeks. But parents are given options either to pay or not. To the customers who are parents, in this case, it might sound almost free when they consider the benefits. The price makes the services more valuable to the customers. On the other, the price is the essential weapon that can easily change the market system of the product easily (Lam, 2009). Though Urban Promise offers free services, but that does not really free as an organization. The organization suffers a lot to make sure it is working hard to fundraise in order to cover other costs that go for free to the customers. In fact, Urban Promise understands that families whom they work could not manage to pay for services if offer. Again its goal was to penetrate into the community with the gospel. Afterschool was indirectly used to offer other services to the young people. How is the program promoted in the inner city? Promotion Promotion is also called consumer-influencer strategies. Lamb (2009) defines promotions as communication by marketers that informs, persuades, and reminds potential buyers or customers of a product in order to influence their opinion or elicit a response (p.471). Product or service, price, and distribution can literally get into the market points or distribution but the questions still remain. How will the customer know about your products or, your newly established brand and organizations? This is the role of promotions which includes advertising; public relations which help people know you or the products and services (Levens, 2010). How does Urban Promise Wilmington inform, persuades, remind, and educates the customers? Urban Promise uses several ways to educate and inform its customers. In the first place, it uses annual events like Banquet. The Banquet serves three main important roles: fundraise, sell the programs, and invite people for partnership. The event each year brings together more than six hundred people from the different world of the corporate world and nonprofit. Secondly, Urban Promise partners with different churches. Churches have been a powerful tool in informing the mass about the programs offered by organizations. Thirdly, each year Urban Promise go for recruiting in Colleges around the world in its intern program. The organization has people from Finland, Scotland, Chile, and Africa and within states. People who have served with Urban Promise have promoted the organization to the height. Lastly, it also uses internet such as website (www.urbanpromisewilmington.org), blogs, press release, magazines, flyers, and Face book. Multiple ways of promotion in the organization, suggest that customers usually feel, sense, and taste differently on the same product. Promotion strategy is closely related to the process of communication. As human we assign meaning to feelings, ideas, facts, attitudes and emotions (Lamb, p.400 Marketing and communication article, bright space) Place or distribution Place or distribution is an essential part of marketing because without it, products arent available for customers to buy and profit is lost (Levens, 2010 p.152). Further, Levens define distribution as the process of delivering products and services to customers (p.150). We cannot discuss product without considering where the product will be distributed or shared with the customer. Any customer accesses our services through distribution points that are strategically defined. The Afterschool program at Urban Promise Wilmington targets Church-owned facilities as key points of distribution service. Why? The churches in the City of Wilmington are the main partners of Urban Promise which have more customers to buy our services. The Afterschool program is offered in the way that meets the mission of Urban Promise by making the bible the center for counseling. Free Afterschool program and considering the bible as the center for counseling distinguish Urban Promise from its competitors. Urban Promise serves 600 children and youths each year through Afterschool and summer programs. The organization understands that the needs for educational excellence for less privileged families. The programs are offered at the most critical hours from 2:30 pm up to 6:30 pm of which most parents at work. The main competitors are The YMCA, Simply Equal Education, Literacy Delaware, and Jewish Community Center of Delaware, Inc. The stated nonprofits also run similar programs in the same locations. The only different with Urban Promise is the free Afterschool program and focuses on sharing gospel message to the young people and grooms them to become reliable citizens of their families and communities at large. Conclusion The elements of the Market mix are interconnected and missing one can easily affect both the organization and customers. The market mix helps the organization to achieve its mission through well-coordinated market activities such as product, price, promotion, and place or distribution. Products or services are supposed to add good value to the customers. Products or services determine the market. Good product that meets customers needs and satisfaction are likely to fetch high demand. Sometimes the quality of products or services affects price either positive or negative. Customers are accustomed to knowing the benefits of products before they even consider the price. In addition, the products, and price are also determined by the place or distribution. The same products or services can be charged differently depending on the status of the place. Furthermore, the product, price, and place require promotion to inform and persuade the customer to buy the services. Therefore, the goal of the market mix is to meet the needs and satisfaction of the customer. References Lamb, C.W, Hair, J.F McDaniel (2009) Essential of marketing; South-Western, Cengage Learning, United States Levens, M (2010) Marketing: defined, explained, applied. Pearson Prentice Hall, Upper Saddle River, New Jersey, United States Wood, M. B (2011, 4thEd) The Marketing plan; handbook, Pearson Prentice Hall, upper Saddle River, New Jersey www.urbanpromisewilmington.org Lamb, e-chapter13, (2009) Marketing and Advertising article https://eastern.brightspace.com/d2l/le/content/23621/viewContent/613432/View Lamb, e-chapter 3, (2009) Social responsibility, Ethics, Marketing and Environment article https://eastern.brightspace.com/d2l/le/content/23621/viewContent/613429/View

Comparing The Great Santini and Death of a Salesman :: comparison compare contrast essays

Comparing The Great Santini and Death of a Salesman Elementary school taught everyone that to compare and contrast two things, the best way to go about doing that is with a Venn diagram. Truthfully, this is an effective method, but it is quite rudimentary under the circumstances. "The Great Santini" by Pat Conroy and "Death of a Salesman" by Arthur Miller are two books that can become victims of the dreaded Venn diagram. The two stories are accounts of the lives of two families, each living out its version of the American Dream. The focus of both stories is on the father and how he interacts with everyone and everything around him. Bull Meechum of "The Great Santini" is a marine, raising his children as "hogs" and expecting only the best, if not better, from his brood. Willy Loman of "Death of a Salesman" also expects great things from his children, to the point that he refuses to believe that either of his sons is a failure, even when it is clear that they are. Although the two men themselves have many similarities, there are also other similarities between the two stories. One similarity is the role of the first son in the two anecdotes. Also, there is the role of the second child. Finally, both stories involve characters that are realizing what it means to be a man and what responsibilities come with the title. Bull Meechum is the father of four kids: two boys and two girls. His oldest son is Ben, a senior in high school who is well on his way to a career in basketball. As the son of a marine, Ben has been raised to take orders, no matter what the possible consequences may be. At the beginning of the story, Ben is talking to his father about his future. When Ben vehemently expresses his interest in pursuing basketball, Bull protests and reminds his son that he will serve in the marines for his four years, and then he can do whatever he wants. Unfortunately, Ben's basketball calling is cut short because of his father's hot headed insistence that Ben must take out a player on the other team, resulting in a broken arm and Ben's expulsion from the team.

Essay on Picture of Dorian Gray: The Character of Lord Henry Wotten

The Character of Lord Henry Wotten of The Picture of Dorian Gray  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   The purpose of this essay is to explore the character of Lord Henry Wotten, from The Picture of Dorian Gray by Oscar Wilde. Oscar Wilde once said: I only know that Dorian Gray is a classic and deservedly. With this in mind, this essay is aimed at looking at how Lord Henry Wotton manipulates various conversations and how he effects the story with his challenging speeches, which is the reason The Picture of Dorian Gray is a classic. Henry is such a memorable, cleverly developed character, that his influence on the text elevates the novel's value. In the conversations of Lord Henry Wotton and the behaviour of Dorian Gray [Wilde shows that] †¦. self-expression can be turned into an art. - Acroyd. Lord Henry's conversations are used to introduce humour and intelligence to a tragic story. Lord Henry has a cynical view of the opposite sex, and also to marriage or any form of relationship which involves both genders. Henry says: Men marry because they are tired, women, because they are curious: both are disappointed. Henry here is humorously analyzing marriage, and summing it up in one sentence, which is typical of his conversation. He says things quickly and sharply so the story can move on with humour arising from the conversation. In this example Henry is giving quite a bleak outlook on marriage. This theme is explored further when he says: Young men want to be faithful, and are not, old men want to be faithless, and cannot. In this example, Henry explores the driving force between the nature of old and young men, and how they relate to the opposite sex. He uses irony to demonstrate his knowledge of how males relate t... ... parallel, as Henry's influence on Dorian Gray is evident, but Dorian Gray doesn't affect Henry's character at all. The reader also gets a contrast with Basil's relationship to Henry. Basil appears to ignore the humorous speeches that Henry gives by dismissing them as being "not serious" in nature. Because of this, Henry doesn't effect Basil in a negative way, as he does Dorian. Dorian appears to hang on every word that Henry gives, whereas Basil practically ignores what Henry says. Lord Henry's influence in the novel The Picture of Dorian Gray is that is gives a meaningful, ethical story a further contextual layer. Dorian Gray is a superb story, but the character of Lord Henry Wotton is what elevates the novel to its classic status. Works Cited: Wilde, Oscar. The Picture of Dorian Gray; For Love of the King. London: Routledge/Thoemmes Press, 1993.

Drunk Driving is Not a Serious Offense Essay example -- Reduce DUI Pen

Driving under the influence of alcohol (DUI) has become an issue of national concern, a both state and federal levels (2Githens and Sloan 403). Hearty fines, jail time and a revoking of the convict’s license follow most DUI offenses. DUI penalties need to be decreased and cause of conviction needs to be addressed, because people who are not criminals are going to jail, and enduring insurance fees even though these punishments have been shown to not decrease drinking and driving. Officers are given too much discretion to choose who get convicted, and who doesn’t, being convicted of a DUI can be life changing and should not be taken lightly. Most DUI offenses are detected as a result of direct observation of suspicious behavior, which is up to the discretion of the police officer observing the situation. In police initiated stops, the officer is the only witness to see the violation and is given great power in deciding to pull over the driver or not (Mastrofski, Ritti and Snipes 113-148). The police officer also decides if the law will be enforced or not. The main issue with this is that discrimination could occur very easily, because police can be persuaded by certain factors, including race and gender, to decide whether to arrest the driver or not. Police ethnographies suggest that the decision to arrest for common offenses is viewed by officers as part of there everyday work, whereas their superior officers tend to view an arrest as a â€Å"product†, which contributes to the departments identity, its effectiveness, and efficiency (Mastrofski, Ritti and Snipes 115). Differences in views suggest that the officer s out on the street are looking for people to pull over instead of looking for people that they can assist, as the... ..." Philosophy and Public Affairs 1st ser. 23 (1994): 52-73. Web. 2 Nov. 2013. Jones, James D. "Identifying and Prosecuting Persons for Driving under the Influence of Drugs." Public Health Reports 6th ser. 102 (1987): 627-29. Web. 7 Nov. 2013. Mastrofski, Stephen D., Richard R. Ritti, and Jeffrey B. Snipes. "Expectancy Theory and Police Productivity in DUI Enforcement." Law & Society Review 1st ser. 28 (1994): 113-48. Web. 9 Nov. 2013. Ross, Laurence H. "The Neutralization of Severe Penalties: Some Traffic Law Studies." Law & Society 3rd ser. 10 (1976): 403-13. Web. 4 Nov. 2013. Rubenzer, Steven J. "The Standardized Field Sobriety Tests: A Review of Scientific and Legal Issues." Law and Human Sloan, Frank A., and Penny B. Githens. "Drinking, Driving, and the Price of Automobile Insurance." The Journal of Risk and Insurance 61.1 (1994): 33-58. Web. 6 Nov. 2013.

Family Life Course Development

Family Life Course Development Focus & Scope Assumptions These are the assumptions that provide the foundation for Family Life Course Development Theory. 1. Developmental processes are inevitable and important in understanding families. – Individual family members, Interaction between family members, Structure of family, and The norms composing expectations about family roles all change over time. These changing roles and expectations for different stages of family are viewed as essential to an understanding of the family. . The family group is affected by all the levels of analysis. Social system (Institutional norms and conventions about the family) e. g. legal expectations like child abuse laws Aggregate Clusters (Families and norms structured by class and ethnicity) Social group – Family Sub-group – Relationships (e. g. Husband -Wife, Siblings, etc. ) Individual These general social norms represent the level of analysis of the family as a social institution. This institutional level of analysis is generally the one we refer to when we talk about â€Å"The Family† and is the level on which we often conduct cross-cultural comparisons (the U. S. family compared with the Japanese family). 3. Time is Multi-Dimensional Periodicity – An equal interval of time between each event on the clock. (e. g. jewel movements of a wrist watch‘s gears) However, our experience of time is perhaps not as regimented as periodicity would lead us to believe. Social Process Time- Family and personal experiences are used as a separate way to divide up time. (e. g. â€Å"When we first married† or â€Å"Before your sister was born†) Social norms are tied more closely to this social process dimension of time than to calendar or wristwatch time. Subsequently, for Family Life Course Development Theory, the family process dimension of time is critical to understanding and explaining family change because it provides the marker events for analyses. (E. g. births, weddings, deaths, etc. )

Ch notes

Indians and Africans) b) Factors that hindered unity among the Europeans in America 1. Puritans carved tight, pious, and relatively democratic communities of small family farms A homogeneous world compared to most southern colonies 2. Anglicans built plantations along the coast Where they lorded over a labor force of black slaves Looked down upon the poor white farmers who settled the backcountry 3. Diversity reigned in middle colonies Well-to-do merchants put their stamp on New York City In the countryside sprawling estates were interspersed with modest homesteads 4.Within Individual colonies, conflicts festered over economic Interests, ethnic rivalries, ND religious practices 5. All the clashes made it difficult for colonists to imagine that they were a single people with a common density c) General issues that led colonists to rebel against Brittany 1. The stable arrangement between the colonists and Brittany began to crumble, a victim of the Imperial rivalry between France and Br ittany 2. Once the French were driven from the North American continent, the colonists no longer needed the British for protection 3.The British government made the choice of imposing taxes on colonies that had been accustomed to answering mainly to their win colonial assemblies 4. Issues of taxation, self-rule, and trade restrictions brought the crisis of Imperial authority to a head II. The Shaping of North America: Major geographical features and the importance of the Great Ice Age a) The Rockies, the Sierra Nevada, and Coast Ranges – â€Å"American Mountains† b) The continent was anchored In its Northeastern corner by the massive Canadian Shield c) The â€Å"tidewater† region creased by many river valleys. Loped gently upward to the timeworn ridges of the Appalachians d) â€Å"Roof of America† – the land fell off Jaggedly onto the intermediation Great Basin e) The valleys of Sacramento and San Joaquin Rivers and the Willamette- Peugeot Sound tr ough seamed the Interiors of present-day California, Oregon, and Washington f) When the glaciers finally retreated, they left the North American landscape transformed g) The weight of the ice mantle had depressed the level of the Canadian Shield h) The melting ice had scoured away the shield's topsoil, pitting its rocky surface with thousands of shallow depressions into which the melting glaciers flowed to form lakes l) Deprived of both Inflow and ranging, the giant lake became a gradually shrinking Inland sea. It grew Increasingly saline, slowly evaporated, and left an arid, mineral-rich desert Ill. Peopling the FIFO a) How the ancestors of the American Indians Journeyed to America and why 1 .Some Early peoples may have reached the Americas in crude boats but most probably came by land 2. As the sea level dropped, it exposed a land bridge connecting Eurasia with North America 3. Probably following migratory herds of game, ventured small bands of nomadic Asian hunters b) Evidence th at Indians of Central and South America were advanced 1 . Over the centuries they split into countless tribes, evolved more than 2,000 separate languages, and developed many diverse religions, cultures, and ways of life 2. Their advanced agricultural practices, based primarily on the cultivation of maize 3. These peoples built elaborate cities and carried on far-flung commerce 4.Talented mathematicians, they made strikingly accurate astronomical observations 5. The Aztec sought the favor of the gods by offering human sacrifices Cutting out the hearts of he chests of living victims, who were often captives conquered in battle IV. The Earliest Americans a) Agriculture, especially corn growing, accounted for the size and sophistication of the Native American civilizations in Mexico and South America b) The Nazis built an elaborate pueblo of more than six hundred interconnected rooms c) Maize, strains of beans, and squash made possible â€Å"three-sister† farming, with beans grow ing on the trellis of cornstalks and squash covering the planting mounds to retain moisture in the soil 1 .This produced some of the highest population densities on the continent d) In the northeastern woodlands, the Iroquois Confederacy plopped the political and organizational skills to sustain a robust military alliance that menaced its neighbors e) The native peoples of North America were living in small, scattered, and impermanent settlements f) Women tended to the crops, while men hunted, fished, gathered fuel, and cleared fields for planting g) The Native Americans had neither the desire nor the means to manipulate nature aggressively, they revered the physical world and endowed nature with spiritual properties V. Indirect Discoverers of the New World a) Probably the first Europeans to â€Å"discover† America Blond-bearded Norse seafarers room Scandinavia, who had chanced upon the northeastern shoulder of North America – however, no strong nation-state, yearning to expand, supported these venturesome voyagers. Their flimsy settlements consequently were soon abandoned, and their discovery was forgotten b) Christian Crusaders – European warriors who indirectly discovered America because of Rupee's craving for exotic goods VI.Europeans Enter Africa – Setting the Stage for the â€Å"Discovery' of America a) Marco Polo: an Italian adventurer; he must be regarded as an indirect discoverer of he New World, for his book, with its description of rose- tinted pearls and golden pagodas, stimulated European desires for a cheaper route to the treasures of the East b) The Portuguese not only developed the caravel, but they had discovered that they could return to Europe by sailing northwesterly from the African coast toward the Azores, where the prevailing westward breezes would carry them home c) The participants of the earliest African slave trade were Arab flesh merchants and Africans themselves. 1 . Slave brokers deliberately separated persons from the same rib's and mixed unlike people together to frustrate organized resistance d) Portuguese: they built their own systematic traffic in slaves to work the sugar 1. Bartholomew Aids rounded the southernmost tip of the â€Å"Dark Continent† 2. Vases dad Gamma finally reached India and returned home with a small but tantalizing cargo of Jewels and spices VI'.Columbus Comes upon a New World a) In Spain, a modern national state was taken shape, with the unity, wealth and power to shoulder the formidable tasks of discovery, conquest, and colonization b) The renaissance in the fourteenth century nurtured an ambitious spirit of optimism ND adventure – printing presses facilitated the spread of scientific knowledge. The mariner's compass eliminated some of the uncertainties odd sea travel c) Columbus' voyages to America 1. Where in America? – An island in the Bahamas 2. Columbus was a â€Å"successful failure† because when seeking a new water rou te to the fabled Indies, he in fact bumped into an enormous land barrier blocking the ocean pathway d) Columbus' discovery convulsed four continents: Europe, Africa, and the Americas which emerged and interdependent global economic system 1 . Europe provided the markets, the capital, and the technology 2. Africa furnished the labor 3. The New World offered its raw materials VIII.When Worlds Collide: â€Å"Columbian Exchange† a) Europeans found iguanas and rattlesnakes along with tobacco, beans, maize, tomatoes, and potatoes – eventually revolutionized the international economy as well as the European diet b) The Europeans brought cattle, swine, horses, sugarcane, and the seeds of Kentucky Bluegrass, dandelions, and daisies – the Native Americans adopted the horse, transforming their cultures into highly mobile, wide-ranging hunter societies c) The Europeans brought smallpox, yellow fever, and malaria to the New World, which would quickly devastate the Native Ame ricans. The disease syphilis was brought to the Old World. This had injected the sexually transmitted disease into Europe for the first time. ‘X. The Spanish Conquistadors a) Treaty of Tortillas – divided the â€Å"heathen lands† of the New World between Portugal and Spain b) Important Spanish Explorers 1. Vases Nuke Balboa hailed as the discoverer of the pacific ocean 2. Ferdinand Magellan completed the first circumnavigation of the globe 3. Juan Pence De Leon explored Florida 4.Francisco Coronado went from Arizona to Kansas, while discovering the Grand Canyon and massive herds of Bison 5. Hernandez De Sotto discovered and crossed the Mississippi River 6. Francisco Pizzeria crushed the Incas of Peru and added a huge hoard of booty to Spanish coffers c) Because of the Spanish conquests, the world economy was transformed – it led to more money in Europe which led to the spread of commerce and manufacturing d) Encomia system – it allowed the governmen t to â€Å"commend† or give, Indians to certain colonists in return to try to Christianize them X. The Conquest of Mexico language of the powerful Aztec rulers of the great empire in the highlands of centralMexico b) Cortes' incentive was that he only wanted gold c) Mastectomy believed that Cortes was the god Sequestrate d) Ethnocentric – it amazed the Spanish because of how large and beautiful it was: with 300,000 inhabitants spread over ten square miles; it was surrounded floating gardens odd extraordinary beauty e) Enoch Tries: (Sad Night) the Aztec attacked, driving the Spanish down the causeways from Ethnocentric in a frantic, bloody retreat f) Impact of conquest of Aztec: 1. – : Native population of Mexico decreased rapidly due to disease 2. +: Crops and animals were brought to the Americas as well as language, laws, customs, and religion g) Did De la Razz – the birthday off wholly new race of people X'.Spanish Conquistadors (â€Å"Makers of Americ a†) a) Conquistadores were nobles – about half were professional soldiers and sailors; the rest were peasants, artisans, and members of the middling class b) Personal motives – some wanted royal titles and favors, others wanted to ensure God's favor, some hoped to escape dubious pasts, and some Just wanted adventure c) Conquistadores were armed with horses and gunpowder, as well as preceded by asses; this helped them overpower the Indians d) Most conquistadores did not strike it rich because even if an expedition captured exceptionally rich booty, it was not divided evenly e) Messiest – the â€Å"new race† formed a cultural and a biological bridge between Latin America's European and Indian races XII. The Spread of Spanish America a) The upstart English sent John Callout to explore the northeastern coast of North America b) Jacques Carrier Journeyed hundreds of miles up the SST.Lawrence River c) With the intention of protection, the Spanish began to fortify and settle in the North American borderlands d) In the Battle of Coma in 1599, the Spanish severed one foot of each survivor e) During the Pope's Rebellion in 1680, the pueblo rebels destroyed every Catholic church in the province and killed a score of priests and hundreds of Spanish settlers f) Father Junipers Sera founded at San Diego the first of a chain of twenty-one missions g) The â€Å"Black Legend† – means killing for Christ: the authors describe it as a false concept. They say that despite the mass killings, the Spanish did so many other good things that the good out weighs the bad.

The Return: Midnight Chapter 9

Damon dropped his hand. He simply couldn't make himself do it. Bonnie was weak, light-headed, a liability in combat, easy to confuse – That's it, he thought. I'l use that! She's so naive – â€Å"Let go for a second,†he coaxed. â€Å"So I can get the stave – â€Å" â€Å"No! You'l jump if I do! What's a stave?†Bonnie said, al in one breath. – and stubborn, and impractical – Was the bril iant light beginning to flicker? â€Å"Bonnie,†he said in a low voice, â€Å"I am deadly serious here. If you don't let go, I'l make you – and you won't like that, I promise.† â€Å"Do what he says,†Meredith pleaded from somewhere quite close. â€Å"Bonnie, he's going into the Dark Dimension! But you're going to end up going with him – and you'l both be human slaves this time! Take my hand!† â€Å"Take her hand!†Damon roared, as the light definitely flickered, for an instant becoming less blinding. He could feel Bonnie shifting and trying to see where Meredith was, and then he heard her say, â€Å"I can't – â€Å" And then they were fal ing. The last time they had traveled through a Gate they had been total y enclosed in an elevator-like box. This time they were simply flying. There was the light, and there were the two of them, and they were so blinded that somehow speaking didn't seem possible. There was only the bril iant, fluctuating, beautiful light – And then they were standing in an al ey, so narrow that it just barely al owed the two of them to face each other, and between buildings so high that there was almost no light down where they were. No – that wasn't the reason, Damon thought. He remembered that blood-red perpetual light. It wasn't coming directly from either side of the narrow slit of al ey, which meant that they were basical y in deep burgundy twilight. â€Å"Do you realize where we are?†Damon demanded in a furious whisper. Bonnie nodded, seeming happy about having figured that out already. â€Å"We're basical y in deep burgundy – â€Å" â€Å"Crap!† Bonnie looked around. â€Å"I don't smel anything,†she offered cautiously, and examined the soles of her feet. â€Å"We are,†Damon said slowly and quietly, as if he needed to calm himself between every word, â€Å"in a world where we can be flogged, flayed, and decapitated just for stepping on the ground.† Bonnie tried a little hop and then a jump in place, as if diminishing her ground-interaction time might help them in some manner. She looked at him for further instructions. Quite suddenly, Damon picked her up and stared at her hard, as revelation dawned. â€Å"You're drunk!†he final y whispered. â€Å"You're not even awake! Al this while I've been trying to get you to see sense, and you're a drunken sleepwalker!† â€Å"I am not!†Bonnie said. â€Å"And†¦just in case I am, you ought to be nicer to me. You made me this way.† Some distant part of Damon agreed that this was true. He was the one who'd gotten the girl drunk and then drugged her with truth serum and sleeping medicine. But that was simply a fact, and had nothing to do with how he felt about it. How he felt was that there was no possible way for him to proceed with this al -too-gentle creature along. Of course, the sensible thing would be to get away from her very quickly, and let the city, this huge metropolis of evil, swal ow her in its great, black-fanged maw, as it would most certainly do if she walked a dozen steps on its streets without him. But, as before, something inside him simply wouldn't let him do it. And, he realized, the sooner he admitted that, the sooner he could find a place to put her and begin taking care of his own affairs. â€Å"What's that?†he said, taking one of her hands. â€Å"My opal ring,†Bonnie said proudly. â€Å"See, it goes with everything, because it's al colors. I always wear it; it's casual or dress-up.†She happily let Damon take it off and examine it. â€Å"These are real diamonds on the sides?† â€Å"Flawless, pure white,†Bonnie said, stil proudly. â€Å"Lady Ulma's fianceLucen made it so that if we ever needed to take the stones out and sel them – â€Å"She came up short. â€Å"You're going to take the stones out and sel them! No! No no no no no!† â€Å"Yes! I have to, if you're going to have any chance of surviving,†Damon said. â€Å"And if you say one more word or fail to do exactly as I tel you, I am going to leave you alone here. And then you wil die. â€Å"He turned narrowed, menacing eyes on her. Bonnie abruptly turned into a frightened bird. â€Å"Al right,†she whispered, tears gathering on her eyelashes. â€Å"What's it for?† Thirty minutes later, she was in prison; or as good as. Damon had instal ed her in a second-story apartment with one window covered by rol er blinds, and strict instructions about keeping them down. He had pawned the opal and a diamond successful y, and paid a sour, humorless-looking landlady to bring Bonnie two meals a day, escort her to the toilet when necessary, and otherwise forget about her existence. â€Å"Listen,†he said to Bonnie, who was stil crying silently after the landlady had left them, â€Å"I'l try to get back to see you within three days. If I don't come within a week it'l mean I'm dead. Then you – don't cry! Listen! – then you need to use these jewels and this money to try to get al the way from here to here; where Lady Ulma wil stil be – we hope.† He gave her a map and a little moneybag ful of coins and gems left over from the cost of her bread and board. â€Å"If that happens – and I can pretty wel promise it won't, your best chance is to try walking in the daytime when things are busy; keep your eyes down, your aura smal , and don't talk to anyone. Wear this sacking smock, and carry this bag of food. Pray that nobody asks you anything, but try to look as if you're on an errand for your master. Oh, yes.†Damon reached into his jacket pocket and pul ed out two smal iron slave bracelets, bought when he had gotten the map. â€Å"Never take them off, not when you're sleeping, not when you're eating – never.† He looked at her darkly, but Bonnie was already on the threshold of a panic attack. She was trembling and crying, but too frightened to say a word. Ever since entering the Dark Dimension she'd been keeping her aura as smal as possible, her psychic defenses high; she didn't need to be told to do that. She was in danger. She knew it. Damon finished somewhat more leniently. â€Å"I know it sounds difficult, but I can tel you that I personal y have no intention whatsoever of dying. I'l try to visit you, but getting across the borders of the various sectors is dangerous, and that's what I may have to do to come here. Just be patient, and you'l be al right. Remember, time passes differently here than back on Earth. We can be here for weeks and we'l get back practical y the instant we set out. And, look† – Damon gestured around the room – â€Å"dozens of star bal s! You can watch al of them.† These were the more common kind of star bal , the kind that had, not Power in them, but memories, stories, or lessons. When you held one to your temple, you were immersed in whatever material had been imprinted on the bal . â€Å"Better than TV,†Damon said. â€Å"Much.† Bonnie nodded slightly. She was stil crushed, and she was so smal , so slight, her skin so pale and fine, her hair such a flame of bril iance in the dim crimson light that seeped through the blinds, that as always Damon found himself melting slightly. â€Å"Do you have any questions?†he asked her final y. Bonnie said slowly, â€Å"And – you're going to be†¦?† â€Å"Out getting the vampire versions of Who's Who and the Book of Peers,†Damon said. â€Å"I'm looking for a lady of quality.† After Damon had left, Bonnie looked around the room. It was horrible. Dark brown and just horrible! She had been trying to save Damon from going back into the Dark Dimension because she remembered the terrible way that slaves – who were mostly humans – were treated. But did he appreciate that? Did he? Not in the slightest! And then when she'd been fal ing through the light with him, she'd thought that at least they would be going to Lady Ulma's, the Cinderel a-story woman whom Elena had rescued and who had then regained her wealth and status and had designed beautiful dresses so that the girls could go to fancy parties. There would have been big beds with satin sheets and maids who brought strawberries and clotted cream for breakfast. There would have been sweet Lakshmi to talk to, and gruff Dr. Meggar, and†¦ Bonnie looked around the brown room and the plain rush-fil ed pal et with its single blanket. She picked up a star bal listlessly, and then let it drop from her fingers. Suddenly, a great sleepiness fil ed her, making her head swim. It was like a fog rol ing in. There was absolutely no question of fighting it. Bonnie stumbled toward the bed, fel onto it, and was asleep almost before she had settled under the blanket. â€Å"It's my fault far more than yours,†Stefan was saying to Meredith. â€Å"Elena and I were – deeply asleep – or he'd never have managed any part of it. I'd have noticed him talking with Bonnie. I'd have realized he was taking you hostage. Please don't blame yourself, Meredith.† â€Å"I should have tried to warn you. I just never expected Bonnie to come running out and grab him,†Meredith said. Her dark gray eyes shimmered with unshed tears. Elena squeezed her hand, sick in the pit of her stomach herself. â€Å"You certainly couldn't be expected to fight off Damon,†Stefan said flatly. â€Å"Human or vampire – he's trained; he knows moves that you could never counter. You can't blame yourself.† Elena was thinking the same thing. She was worried about Damon's disappearance – and terrified for Bonnie. Yet at another level of her mind she was wondering at the lacerations on Meredith's palm that she was trying to warm. The strangest thing was that the wounds appeared to have been treated – rubbed slick with lotion. But she wasn't going to bother Meredith about it at a time like this. Especial y when it was real y Elena's own fault. She was the one who had enticed Stefan the night before. Oh, they had been deep, al right – deep in each other's minds. â€Å"Anyway, it's Bonnie's fault if it's anyone's,†Stefan said regretful y. â€Å"But now I'm worried about her. Damon's not going to be inclined to watch out for her if he didn't want her to come.† Meredith bowed her head. â€Å"It's my fault if she gets hurt.† Elena chewed her lower lip. There was something wrong. Something about Meredith, that Meredith wasn't tel ing her. Her hands were real y damaged, and Elena couldn't figure out how they could have gotten that way. Almost as if she knew what Elena was thinking, Meredith slipped her hand out of Elena's and looked at it. Looked at both her palms, side by side. They were equal y scratched and torn. Meredith bent her dark head farther, almost doubling over where she sat. Then she straightened, throwing back her head like someone who had made a decision. She said, â€Å"There's something I have to tel you – â€Å" â€Å"Wait,†Stefan whispered, putting a hand on her shoulder. â€Å"Listen. There's a car coming.† Elena listened. In a moment she heard it too. â€Å"They're coming to the boardinghouse,†she said, puzzled. â€Å"It's so early,†Meredith said. â€Å"Which means – â€Å" â€Å"It has to be the police after Matt,†Stefan finished. â€Å"I'd better go in and wake him up. I'l put him in the root cel ar.† Elena quickly corked the star bal with its meager ounces of fluid. â€Å"He can take this with him,†she was beginning, when Meredith suddenly ran to the opposite side of the Gate. She picked up a long, slender object that Elena couldn't recognize, even with Power channeled to her eyes. She saw Stefan blink and stare at it. â€Å"This needs to go in the root cel ar too,†Meredith said. â€Å"And there are probably earth tracks coming out of the cel ar, and blood in the kitchen. Two places.† â€Å"Blood?†Elena began, furious with Damon, but then she shook her head and refocused. In the light of dawn, she could see a police car, cruising like some great white shark toward the house. â€Å"Let's go,†Elena said. â€Å"Go, go, go!† They al dashed back to the boardinghouse, crouching to stay low to the ground as they did it. As they went, Elena hissed, â€Å"Stefan, you've got to Influence them if you can. Meredith, you try to clean up the soil and blood. I'l get Matt; he's less likely to punch me when I tel him he has to hide.† They hastened to their appointed duties. In the middle of it al , Mrs. Flowers appeared, dressed in a flannel nightgown with a fuzzy pink robe over it, and slippers with bunny heads on them. As the first hammering knock on the door sounded, she had her hand on the door handle, and the police officer, who was beginning to shout, â€Å"POLICE! OPEN THE – â€Å"found himself bawling this directly over the head of a little old lady who could not have looked more frail or harmless. He ended almost in a whisper, † – door?† â€Å"It is open,†Mrs. Flowers said sweetly. She opened it to its widest, so that Elena could see two officers, and the officers could see Elena, Stefan, and Meredith, al of whom had just arrived from the kitchen area. â€Å"We want to speak to Matt Honeycutt,†the female officer said. Elena noted that the squad car was from the Ridgemont Sheriff's Department. â€Å"His mother informed us that he was here – after serious questioning.† They were coming inside, shouldering their way past Mrs. Flowers. Elena glanced at Stefan, who was pale, with tiny beads of sweat visible on his forehead. He was looking intently at the female officer, but she just kept talking. â€Å"His mother says he's been virtual y living at this boardinghouse recently,†she said, while the male officer held up some kind of paperwork. â€Å"We have a warrant to search the premises,†he said flatly. Mrs. Flowers seemed uncertain. She glanced back toward Stefan, but then let her gaze move on to the other teenagers. â€Å"Perhaps it would be best if I made everyone a nice cup of tea?† Stefan was stil looking at the woman, his face looking paler and more drawn than ever. Elena felt a sudden panic clutch at her stomach. Oh, God, even with the gift of her blood tonight, Stefan was weak – far too weak to even use Influence. â€Å"May I ask a question?†Meredith said in her low, calm voice. â€Å"Not about the warrant,†she added, waving the paper away. â€Å"How is it out there in Fel ‘s Church? Do you know what's going on?† She was buying time, Elena thought, and yet everyone stopped to hear the answer. â€Å"Mayhem,†the female sheriff replied after a moment's pause. â€Å"It's like a war zone out there. Worse than that because it's the kids who are – â€Å"She broke off and shook her head. â€Å"That's not our business. Our business is finding a fugitive from justice. But first, as we were driving toward your hotel we saw a very bright column of light. It wasn't from a helicopter. I don't suppose you know anything about what it was?† Just a door through space and time, Elena was thinking, as Meredith answered, stil calmly, â€Å"Maybe a power transmitter blowing up? Or a freak shaft of lightning? Or are you talking about†¦a UFO?†She lowered her already soft voice. â€Å"We don't have time for this,†the male sheriff said, looking disgusted. â€Å"We're here to find this Honeycutt man.† â€Å"You're welcome to look,†Mrs. Flowers said. They were already doing so. Elena felt shocked and nauseated on two fronts. â€Å"This Honeycutt man.†Man, not boy. Matt was over eighteen. Was he stil a juvenile? If not, what would they do to him when they eventual y caught up to him? And then there was Stefan. Stefan had been so certain, so†¦ convincing†¦in his announcements about being wel again. Al that talk about going back to hunting animals – but the truth was that he needed much more blood to recover. Now her mind spun into planning mode, faster and faster. Stefan obviously wasn't going to be able to Influence both of those officers without a very large donation of human blood. And if Elena gave it†¦the sick feeling in her stomach increased and she felt the smal hairs on her body stand up†¦if she gave it, what were the chances that she would become a vampire herself? High, a cool, rational voice in her mind answered. Very high, considering that less than a week ago, she had been exchanging blood with Damon. Frequently. Uninhibitedly. Which left her with the only plan she could think of. These sheriffs wouldn't find Matt, but Meredith and Bonnie had told her the whole story of how another Ridgemont sheriff had come, asking about Matt – and about Stefan's girlfriend. The problem was that she, Elena Gilbert, had â€Å"died†nine months ago. She shouldn't be here – and she had a feeling that these officers would be inquisitive. They needed Stefan's Power. Right now. There was no other way, no other choice. Stefan. Power. Human blood. She moved to Meredith, who had her dark head down and cocked to one side as if listening to the two sheriffs clomping above on the stairs. â€Å"Meredith – â€Å" Meredith turned toward her and Elena almost took a step back in shock. Meredith's normal y olive complexion was gray, and her breath was coming fast and shal owly. Meredith, calm and composed Meredith, already knew what Elena was going to ask of her. Enough blood to leave her out of control as it was being taken. And fast. That terrified her. More than terrified. She can't do it, Elena thought. We're lost.

Bayesian Inference

Biostatistics (2010), 11, 3, pp. 397–412 doi:10. 1093/biostatistics/kxp053 Advance Access publication on December 4, 2009 Bayesian inference for generalized linear mixed models YOUYI FONG Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 Department of Biostatistics, University of Washington, Seattle, WA 98112, USA ? HAVARD RUE Department of Mathematical Sciences, The Norwegian University for Science and Technology, N-7491 Trondheim, Norway JON WAKEFIELD? Departments of Statistics and Biostatistics, University of Washington, Seattle, WA 98112, USA [email  protected] ashington. edu S UMMARY Generalized linear mixed models (GLMMs) continue to grow in popularity due to their ability to directly acknowledge multiple levels of dependency and model different data types. For small sample sizes especially, likelihood-based inference can be unreliable with variance components being particularly difficult to estimate. A Bayesian approach is appealing but has been hampered by the lack of a fast implementation, and the difficulty in specifying prior distributions with variance components again being particularly problematic.Here, we briefly review previous approaches to computation in Bayesian implementations of GLMMs and illustrate in detail, the use of integrated nested Laplace approximations in this context. We consider a number of examples, carefully specifying prior distributions on meaningful quantities in each case. The examples cover a wide range of data types including those requiring smoothing over time and a relatively complicated spline model for which we examine our prior specification in terms of the implied degrees of freedom.We conclude that Bayesian inference is now practically feasible for GLMMs and provides an attractive alternative to likelihood-based approaches such as penalized quasi-likelihood. As with likelihood-based approaches, great care is required in the analysis of clustered bina ry data since approximation strategies may be less accurate for such data. Keywords: Integrated nested Laplace approximations; Longitudinal data; Penalized quasi-likelihood; Prior specification; Spline models. 1.I NTRODUCTION Generalized linear mixed models (GLMMs) combine a generalized linear model with normal random effects on the linear predictor scale, to give a rich family of models that have been used in a wide variety of applications (see, e. g. Diggle and others, 2002; Verbeke and Molenberghs, 2000, 2005; McCulloch and others, 2008). This flexibility comes at a price, however, in terms of analytical tractability, which has a ? To whom correspondence should be addressed. c The Author 2009. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals. [email  protected] rg. 398 Y. F ONG AND OTHERS number of implications including computational complexity, and an unknown degree to which inference is dependent on modeling assumptions. Lik elihood-based inference may be carried out relatively easily within many software platforms (except perhaps for binary responses), but inference is dependent on asymptotic sampling distributions of estimators, with few guidelines available as to when such theory will produce accurate inference. A Bayesian approach is attractive, but requires the specification of prior distributions which is not straightforward, in particular for variance components.Computation is also an issue since the usual implementation is via Markov chain Monte Carlo (MCMC), which carries a large computational overhead. The seminal article of Breslow and Clayton (1993) helped to popularize GLMMs and placed an emphasis on likelihood-based inference via penalized quasi-likelihood (PQL). It is the aim of this article to describe, through a series of examples (including all of those considered in Breslow and Clayton, 1993), how Bayesian inference may be performed with computation via a fast implementation and with guidance on prior specification. The structure of this article is as follows.In Section 2, we define notation for the GLMM, and in Section 3, we describe the integrated nested Laplace approximation (INLA) that has recently been proposed as a computationally convenient alternative to MCMC. Section 4 gives a number of prescriptions for prior specification. Three examples are considered in Section 5 (with additional examples being reported in the supplementary material available at Biostatistics online, along with a simulation study that reports the performance of INLA in the binary response situation). We conclude the paper with a discussion in Section 6. 2.T HE G ENERALIZED LINEAR MIXED MODEL GLMMs extend the generalized linear model, as proposed by Nelder and Wedderburn (1972) and comprehensively described in McCullagh and Nelder (1989), by adding normally distributed random effects on the linear predictor scale. Suppose Yi j is of exponential family form: Yi j |? i j , ? 1 ? p(â₠¬ ¢), where p(†¢) is a member of the exponential family, that is, p(yi j |? i j , ? 1 ) = exp yi j ? i j ? b(? i j ) + c(yi j , ? 1 ) , a(? 1 ) Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 for i = 1, . . . , m units (clusters) and j = 1, . . , n i , measurements per unit and where ? i j is the (scalar) ? canonical parameter. Let ? i j = E[Yi j |? , b i , ? 1 ] = b (? i j ) with g(? i j ) = ? i j = x i j ? + z i j b i , where g(†¢) is a monotonic â€Å"link† function, x i j is 1 ? p, and z i j is 1 ? q, with ? a p ? 1 vector of fixed ? Q effects and b i a q ? 1 vector of random effects, hence ? i j = ? i j (? , b i ). Assume b i |Q ? N (0, Q ? 1 ), where ? the precision matrix Q = Q (? 2 ) depends on parameters ? 2 . For some choices of model, the matrix Q is singular; examples include random walk models (as considered in Section 5. ) and intrinsic conditional ? autoregressive models. We further assume tha t ? is assigned a normal prior distribution. Let ? = (? , b ) denote the G ? 1 vector of parameters assigned Gaussian priors. We also require priors for ? 1 (if not a constant) and for ? 2 . Let ? = (? 1 , ? 2 ) be the variance components for which non-Gaussian priors are ? assigned, with V = dim(? ). 3. I NTEGRATED NESTED L APLACE APPROXIMATION Before the MCMC revolution, there were few examples of the applications of Bayesian GLMMs since, outside of the linear mixed model, the models are analytically intractable.Kass and Steffey (1989) describe the use of Laplace approximations in Bayesian hierarchical models, while Skene and Wakefield Bayesian GLMMs 399 (1990) used numerical integration in the context of a binary GLMM. The use of MCMC for GLMMs is particularly appealing since the conditional independencies of the model may be exploited when the required conditional distributions are calculated. Zeger and Karim (1991) described approximate Gibbs sampling for GLMMs, with nonstandar d conditional distributions being approximated by normal distributions.More general Metropolis–Hastings algorithms are straightforward to construct (see, e. g. Clayton, 1996; Gamerman, 1997). The winBUGS (Spiegelhalter, Thomas, and Best, 1998) software example manuals contain many GLMM examples. There are now a variety of additional software platforms for fitting GLMMs via MCMC including JAGS (Plummer, 2009) and BayesX (Fahrmeir and others, 2004). A large practical impediment to data analysis using MCMC is the large computational burden. For this reason, we now briefly review the INLA computational approach upon which we concentrate.The method combines Laplace approximations and numerical integration in a very efficient manner (see Rue and others, 2009, for a more extensive treatment). For the GLMM described in Section 2, the posterior is given by m Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 ? y ? ? ? ?(? , ? |y ) ? ?(? |? )? (? ) i=1 y ? p(y i |? , ? ) m i=1 1 ? ? Q ? ? b ? ?(? )? (? )|Q (? 2 )|1/2 exp ? b T Q (? 2 )b + 2 y ? log p(y i |? , ? 1 ) , where y i = (yi1 , . . . , yin i ) is the vector of observations on unit/cluster i.We wish to obtain the posterior y y marginals ? (? g |y ), g = 1, . . . , G, and ? (? v |y ), v = 1, . . . , V . The number of variance components, V , should not be too large for accurate inference (since these components are integrated out via Cartesian product numerical integration, which does not scale well with dimension). We write y ? (? g |y ) = which may be evaluated via the approximation y ? (? g |y ) = K ? ? y ? ?(? g |? , y ) ? ?(? |y )d? , ? ? y ? ?(? g |? , y ) ? ? (? |y )d? ? y ? ? (? g |? k , y ) ? ? (? k |y ) ? k, ? (3. 1) k=1 here Laplace (or other related analytical approximations) are applied to carry out the integrations required ? ? for evaluation of ? (? g |? , y ). To produce the grid of points {? k , k = 1, . . . , K } over which numerical inte? y gration is performed, the mode of ? (? |y ) is located, and the Hessian is approximated, from which the grid is created and exploited in (3. 1). The output of INLA consists of posterior marginal distributions, which can be summarized via means, variances, and quantiles. Importantly for model comparison, the normaly izing constant p(y ) is calculated.The evaluation of this quantity is not straightforward using MCMC (DiCiccio and others, 1997; Meng and Wong, 1996). The deviance information criterion (Spiegelhalter, Best, and others, 1998) is popular as a model selection tool, but in random-effects models, the implicit approximation in its use is valid only when the effective number of parameters is much smaller than the number of independent observations (see Plummer, 2008). 400 Y. F ONG AND OTHERS 4. P RIOR DISTRIBUTIONS 4. 1 Fixed effects Recall that we assume ? is normally distributed. Often there will be sufficient information in the data for ? o be well estimated with a n ormal prior with a large variance (of course there will be circumstances under which we would like to specify more informative priors, e. g. when there are many correlated covariates). The use of an improper prior for ? will often lead to a proper posterior though care should be taken. For example, Wakefield (2007) shows that a Poisson likelihood with a linear link can lead to an improper posterior if an improper prior is used. Hobert and Casella (1996) discuss the use of improper priors in linear mixed effects models.If we wish to use informative priors, we may specify independent normal priors with the parameters for each component being obtained via specification of 2 quantiles with associated probabilities. For logistic and log-linear models, these quantiles may be given on the exponentiated scale since these are more interpretable (as the odds ratio and rate ratio, respectively). If ? 1 and ? 2 are the quantiles on the exponentiated scale and p1 and p2 are the associated probab ilities, then the parameters of the normal prior are given by ? = ? = z 2 log(? 1 ) ? z 1 log(? 2 ) , z2 ? 1 Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 log(? 2 ) ? log(? 1 ) , z2 ? z1 where z 1 and z 2 are the p1 and p2 quantiles of a standard normal random variable. For example, in an epidemiological context, we may wish to specify a prior on a relative risk parameter, exp(? 1 ), which has a median of 1 and a 95% point of 3 (if we think it is unlikely that the relative risk associated with a unit increase in exposure exceeds 3). These specifications lead to ? 1 ? N (0, 0. 6682 ). 4. 2 Variance componentsWe begin by describing an approach for choosing a prior for a single random effect, based on Wakefield (2009). The basic idea is to specify a range for the more interpretable marginal distribution of bi and use this to drive specification of prior parameters. We state a trivial lemma upon which prior specification is ba sed, but first define some notation. We write ? ? Ga(a1 , a2 ) for the gamma distribution with un? normalized density ? a1 ? 1 exp(? a2 ? ). For q-dimensional x , we write x ? Tq (? , , d) for the Student’s x x t distribution with unnormalized density [1 + (x ? ? )T ? 1 (x ? )/d]? (d+q)/2 . This distribution has location ? , scale matrix , and degrees of freedom d. L EMMA 1 Let b|? ? N (0, ? ?1 ) and ? ? Ga(a1 , a2 ). Integration over ? gives the marginal distribution of b as T1 (0, a2 /a1 , 2a1 ). To decide upon a prior, we give a range for a generic random effect b and specify the degrees of freev d dom, d, and then solve for a1 and a2 . For the range (? R, R), we use the relationship  ±t1? (1? q)/2 a2 /a1 = d  ±R, where tq is the 100 ? qth quantile of a Student t random variable with d degrees of freedom, to give d a1 = d/2 and a2 = R 2 d/2(t1? (1? q)/2 )2 .In the linear mixed effects model, b is directly interpretable, while for binomial or Poisson models, it is more appropriate to think in terms of the marginal distribution of exp(b), the residual odds and rate ratio, respectively, and this distribution is log Student’s t. For example, if we choose d = 1 (to give a Cauchy marginal) and a 95% range of [0. 1, 10], we take R = log 10 and obtain a = 0. 5 and b = 0. 0164. Bayesian GLMMs 401 ?1 Another convenient choice is d = 2 to give the exponential distribution with mean a2 for ? ?2 . This leads to closed-form expressions for the more interpretable quantiles of ? o that, for example, if we 2 specify the median for ? as ? m , we obtain a2 = ? m log 2. Unfortunately, the use of Ga( , ) priors has become popular as a prior for ? ?2 in a GLMM context, arising from their use in the winBUGS examples manual. As has been pointed out many times (e. g. Kelsall and Wakefield, 1999; Gelman, 2006; Crainiceanu and others, 2008), this choice places the majority of the prior mass away from zero and leads to a marginal prior for the random effects which is Student’s t with 2 degrees of freedom (so that the tails are much heavier than even a Cauchy) and difficult to justify in any practical setting.We now specify another trivial lemma, but first establish notation for the Wishart distribution. For the q ? q nonsingular matrix z , we write z ? Wishartq (r, S ) for the Wishart distribution with unnormalized Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 Q Lemma: Let b = (b1 , . . . , bq ), with b |Q ? iid Nq (0, Q ? 1 ), Q ? Wishartq (r, S ). Integration over Q b as Tq (0, [(r ? q + 1)S ]? 1 , r ? q + 1). S gives the marginal distribution of The margins of a multivariate Student’s t are t also, which allows r and S to be chosen as in the univariate case.Specifically, the kth element of a generic random effect, bk , follows a univariate Student t distribution with location 0, scale S kk /(r ? q + 1), and degrees of freedom d = r ? q + 1, where S kk d is element (k, k) of the inverse of S . We obtain r = d + q ? 1 and S kk = (t1? (1? q)/2 )2 /(d R 2 ). If a priori b are correlated we may specify S jk = 0 for j = k and we have no reason to believe that elements of S kk = 1/Skk , to recover the univariate specification, recognizing that with q = 1, the univariate Wishart has parameters a1 = r/2 and a2 = 1/(2S).If we believe that elements of b are dependent then we may specify the correlations and solve for the off-diagonal elements of S . To ensure propriety of the posterior, proper priors are required for ; Zeger and Karim (1991) use an improper prior for , so that the posterior is improper also. 4. 3 Effective degrees of freedom variance components prior z z z z density |z |(r ? q? 1)/2 exp ? 1 tr(z S ? 1 ) . This distribution has E[z ] = r S and E[z ? 1 ] = S ? 1 /(r ? q ? 1), 2 and we require r > q ? 1 for a proper distribution.In Section 5. 3, we describe the GLMM representation of a spline model. A generic linear spline model is given by K yi = x i ? + k=1 z ik bk + i , where x i is a p ? 1 vector of covariates with p ? 1 associated fixed effects ? , z ik denote the spline 2 basis, bk ? iid N (0, ? b ), and i ? iid N (0, ? 2 ), with bk and i independent. Specification of a prior for 2 is not straightforward, but may be of great importance since it contributes to determining the amount ? b of smoothing that is applied. Ruppert and others (2003, p. 77) raise concerns, â€Å"about the instability of automatic smoothing parameter selection even for single predictor models†, and continue, â€Å"Although we are attracted by the automatic nature of the mixed model-REML approach to fitting additive models, we discourage blind acceptance of whatever answer it provides and recommend looking at other amounts of smoothing†. While we would echo this general advice, we believe that a Bayesian mixed model approach, with carefully chosen priors, can increase the stability of the mixed model representation. There has be en 2 some discussion of choice of prior for ? in a spline context (Crainiceanu and others, 2005, 2008). More general discussion can be found in Natarajan and Kass (2000) and Gelman (2006). In practice (e. g. Hastie and Tibshirani, 1990), smoothers are often applied with a fixed degrees of freedom. We extend this rationale by examining the prior degrees of freedom that is implied by the choice 402 Y. F ONG AND OTHERS ?2 ? b ? Ga(a1 , a2 ). For the general linear mixed model y = x ? + zb + , we have x z where C = [x |z ] is n ? ( p + K ) and C y = x ? + z b = C (C T C + 0 p? p 0K ? p )? 1 C T y , = 0 p? K 2 cov(b )? 1 b ? )? 1 C T C }, Downloaded from http://biostatistics. xfordjournals. org/ at Cornell University Library on April 20, 2013 (see, e. g. Ruppert and others, 2003, Section 8. 3). The total degrees of freedom associated with the model is C df = tr{(C T C + which may be decomposed into the degrees of freedom associated with ? and b , and extends easily to situations in which we have additional random effects, beyond those associated with the spline basis (such an example is considered in Section 5. 3). In each of these situations, the degrees of freedom associated C with the respective parameter is obtained by summing the appropriate diagonal elements of (C T C + )? C T C . Specifically, if we have j = 1, . . . , d sets of random-effect parameters (there are d = 2 in the model considered in Section 5. 3) then let E j be the ( p + K ) ? ( p + K ) diagonal matrix with ones in the diagonal positions corresponding to set j. Then the degrees of freedom associated with this set is E C df j = tr{E j (C T C + )? 1 C T C . Note that the effective degrees of freedom changes as a function of K , as expected. To evaluate , ? 2 is required. If we specify a proper prior for ? 2 , then we may specify the 2 2 joint prior as ? (? b , ? 2 ) = ? (? 2 )? (? b |? 2 ).Often, however, we assume the improper prior ? (? 2 ) ? 1/? 2 since the data provide sufficient information with respect to ? 2 . Hence, we have found the substitution of an estimate for ? 2 (for example, from the fitting of a spline model in a likelihood implementation) to be a practically reasonable strategy. As a simple nonspline demonstration of the derived effective degrees of freedom, consider a 1-way analysis of variance model Yi j = ? 0 + bi + i j 2 with bi ? iid N (0, ? b ), i j ? iid N (0, ? 2 ) for i = 1, . . . , m = 10 groups and j = 1, . . . , n = 5 observa? 2 tions per group. For illustration, we assume ? ? Ga(0. 5, 0. 005). Figure 1 displays the prior distribution for ? , the implied prior distribution on the effective degrees of freedom, and the bivariate plot of these quantities. For clarity of plotting, we exclude a small number of points beyond ? > 2. 5 (4% of points). In panel (c), we have placed dashed horizontal lines at effective degrees of freedom equal to 1 (complete smoothing) and 10 (no smoothing). From panel (b), we conclude that here the prior choice favors q uite strong smoothing. This may be contrasted with the gamma prior with parameters (0. 001, 0. 001), which, in this example, gives reater than 99% of the prior mass on an effective degrees of freedom greater than 9. 9, again showing the inappropriateness of this prior. It is appealing to extend the above argument to nonlinear models but unfortunately this is not straightforward. For a nonlinear model, the degrees of freedom may be approximated by C df = tr{(C T W C + where W = diag Vi? 1 d? i dh 2 )? 1 C T W C }, and h = g ? 1 denotes the inverse link function. Unfortunately, this quantity depends on ? and b , which means that in practice, we would have to use prior estimates for all of the parameters, which may not be practically possible.Fitting the model using likelihood and then substituting in estimates for ? and b seems philosophically dubious. Bayesian GLMMs 403 Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 Fig. 1. Gamma prior for ? ?2 with parameters 0. 5 and 0. 005, (a) implied prior for ? , (b) implied prior for the effective degrees of freedom, and (c) effective degrees of freedom versus ? . 4. 4 Random walk models Conditionally represented smoothing models are popular for random effects in both temporal and spatial applications (see, e. g. Besag and others, 1995; Rue and Held, 2005).For illustration, consider models of the form ? (m? r ) Q u 2 exp ? p(u |? u ) = (2? )? (m? r )/2 |Q |1/2 ? u 1 T u Qu , 2 2? u (4. 1) 404 Y. F ONG AND OTHERS where u = (u 1 , . . . , u m ) is the collection of random effects, Q is a (scaled) â€Å"precision† matrix of rank Q m ? r , whose form is determined by the application at hand, and |Q | is a generalized determinant which is the product over the m ? r nonzero eigenvalues of Q . Picking a prior for ? u is not straightforward because ? u has an interpretation as the conditional standard deviation, where the elements that are conditioned upon depend s on the application.We may simulate realizations from (4. 1) to examine candidate prior distributions. Due to the rank deficiency, (4. 1) does not define a probability density, and so we cannot directly simulate from this prior. However, Rue and Held (2005) give an algorithm for generating samples from (4. 1): 1. Simulate z j ? N (0, 1 ), for j = m ? r + 1, . . . , m, where ? j are the eigenvalues of Q (there are j m ? r nonzero eigenvalues as Q has rank m ? r ). 2. Return u = z m? r +1 e n? r +1 + z 3 e 3 + †¢ †¢ †¢ + z n e m = E z , where e j are the corresponding eigenvectors of Q , E is the m ? (m ? ) matrix with these eigenvectors as columns, and z is the (m ? r ) ? 1 vector containing z j , j = m ? r + 1, . . . , m. The simulation algorithm is conditioned so that samples are zero in the null-space of Q ; if u is a sample and the null-space is spanned by v 1 and v 2 , then u T v 1 = u T v 2 = 0. For example, suppose Q 1 = 0 so that the null-space is spanned by 1, and the rank deficiency is 1. Then Q is improper since the eigenvalue corresponding to 1 is zero, and samples u produced by the algorithm are such that u T 1 = 0. In Section 5. 2, we use this algorithm to evaluate different priors via simulation.It is also useful to note that if we wish to compute the marginal variances only, simulation is not required, as they are available as the diagonal elements of the matrix j 1 e j e T . j j 5. E XAMPLES Here, we report 3 examples, with 4 others described in the supplementary material available at Biostatistics online. Together these cover all the examples in Breslow and Clayton (1993), along with an additional spline example. In the first example, results using the INLA numerical/analytical approximation described in Section 3 were compared with MCMC as implemented in the JAGS software (Plummer, 2009) and found to be accurate.For the models considered in the second and third examples, the approximation was compared with the MCMC implement ation contained in the INLA software. 5. 1 Longitudinal data We consider the much analyzed epilepsy data set of Thall and Vail (1990). These data concern the number ? of seizures, Yi j for patient i on visit j, with Yi j |? , b i ? ind Poisson(? i j ), i = 1, . . . , 59, j = 1, . . . , 4. We concentrate on the 3 random-effects models fitted by Breslow and Clayton (1993): log ? i j = x i j ? + b1i , (5. 1) (5. 2) (5. 3) Downloaded from http://biostatistics. oxfordjournals. rg/ at Cornell University Library on April 20, 2013 log ? i j = x i j ? + b1i + b2i V j /10, log ? i j = x i j ? + b1i + b0i j , where x i j is a 1 ? 6 vector containing a 1 (representing the intercept), an indicator for baseline measurement, a treatment indicator, the baseline by treatment interaction, which is the parameter of interest, age, and either an indicator of the fourth visit (models (5. 1) and (5. 2) and denoted V4 ) or visit number coded ? 3, ? 1, +1, +3 (model (5. 3) and denoted V j /10) and ? is the associated fixed effect. All 3 models 2 include patient-specific random effects b1i ? N 0, ? , while in model (5. 2), we introduce independent 2 ). Model (5. 3) includes random effects on the slope associated with â€Å"measurement errors,† b0i j ? N (0, ? 0 Bayesian GLMMs 405 Table 1. PQL and INLA summaries for the epilepsy data Variable Base Trt Base ? Trt Age V4 or V/10 ? 0 ? 1 ? 2 Model (5. 1) PQL 0. 87  ± 0. 14 ? 0. 91  ± 0. 41 0. 33  ± 0. 21 0. 47  ± 0. 36 ? 0. 16  ± 0. 05 — 0. 53  ± 0. 06 — INLA 0. 88  ± 0. 15 ? 0. 94  ± 0. 44 0. 34  ± 0. 22 0. 47  ± 0. 38 ? 0. 16  ± 0. 05 — 0. 56  ± 0. 08 — Model (5. 2) PQL 0. 86  ± 0. 13 ? 0. 93  ± 0. 40 0. 34  ± 0. 21 0. 47  ± 0. 35 ? 0. 10  ± 0. 09 0. 36  ± 0. 04 0. 48  ± 0. 06 — INLA 0. 8  ± 0. 15 ? 0. 96  ± 0. 44 0. 35  ± 0. 23 0. 48  ± 0. 39 ? 0. 10  ± 0. 09 0. 41  ± 0. 04 0. 53  ± 0. 07 — Model (5. 3) PQL 0. 87  ± 0. 14 ? 0. 91  ± 0. 41 0. 33  ± 0. 21 0. 46  ± 0. 36 ? 0. 26  ± 0. 16 — 0. 52  ± 0. 06 0. 74  ± 0. 16 INLA 0. 88  ± 0. 14 ? 0. 94  ± 0. 44 0. 34  ± 0. 22 0. 47  ± 0. 38 ? 0. 27  ± 0. 16 — 0. 56  ± 0. 06 0. 70  ± 0. 14 Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 visit, b2i with b1i b2i ? N (0, Q ? 1 ). (5. 4) We assume Q ? Wishart(r, S ) with S = S11 S12 . For prior specification, we begin with the bivariate S21 S22 model and assume that S is diagonal.We assume the upper 95% point of the priors for exp(b1i ) and exp(b2i ) are 5 and 4, respectively, and that the marginal distributions are t with 4 degrees of freedom. Following the procedure outlined in Section 4. 2, we obtain r = 5 and S = diag(0. 439, 0. 591). We take ? 2 the prior for ? 1 in model (5. 1) to be Ga(a1 , a2 ) with a1 = (r ? 1)/2 = 2 and a2 = 1/2S11 = 1. 140 (so that this prior coincides with the marginal prior obtained from the bivariat e specification). In model (5. 2), ? 2 ? 2 we assume b1i and b0i j are independent, and that ? 0 follows the same prior as ? , that is, Ga(2, 1. 140). We assume a flat prior on the intercept, and assume that the rate ratios, exp(? j ), j = 1, . . . , 5, lie between 0. 1 and 10 with probability 0. 95 which gives, using the approach described in Section 4. 1, a normal prior with mean 0 and variance 1. 172 . Table 1 gives PQL and INLA summaries for models (5. 1–5. 3). There are some differences between the PQL and Bayesian analyses, with slightly larger standard deviations under the latter, which probably reflects that with m = 59 clusters, a little accuracy is lost when using asymptotic inference.There are some differences in the point estimates which is at least partly due to the nonflat priors used—the priors have relatively large variances, but here the data are not so abundant so there is sensitivity to the prior. Reassuringly under all 3 models inference for the bas eline-treatment interaction of interest is virtually y identical and suggests no significant treatment effect. We may compare models using log p(y ): for 3 models, we obtain values of ? 674. 8, ? 638. 9, and ? 665. 5, so that the second model is strongly preferred. 5. Smoothing of birth cohort effects in an age-cohort model We analyze data from Breslow and Day (1975) on breast cancer rates in Iceland. Let Y jk be the number of breast cancer of cases in age group j (20–24,. . . , 80–84) and birth cohort k (1840–1849,. . . ,1940–1949) with j = 1, . . . , J = 13 and k = 1, . . . , K = 11. Following Breslow and Clayton (1993), we assume Y jk |? jk ? ind Poisson(? jk ) with log ? jk = log n jk + ? j + ? k + vk + u k (5. 5) and where n jk is the person-years denominator, exp(? j ), j = 1, . . . , J , represent fixed effects for age relative risks, exp(? is the relative risk associated with a one group increase in cohort group, vk ? iid 406 Y. F ONG AND OTHERS 2 N (0, ? v ) represent unstructured random effects associated with cohort k, with smooth cohort terms u k following a second-order random-effects model with E[u k |{u i : i < k}] = 2u k? 1 ? u k? 2 and Var(u k |{u i : 2 i < k}) = ? u . This latter model is to allow the rates to vary smoothly with cohort. An equivalent representation of this model is, for 2 < k < K ? 1, 1 E[u k |{u l : l = k}] = (4u k? 1 + 4u k+1 ? u k? 2 ? u k+2 ), 6 Var(u k |{u l : l = k}) = 2 ? . 6 Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 The rank of Q in the (4. 1) representation of this model is K ? 2 reflecting that both the overall level and the overall trend are aliased (hence the appearance of ? in (5. 5)). The term exp(vk ) reflects the unstructured residual relative risk and, following the argument in Section 4. 2, we specify that this quantity should lie in [0. 5, 2. 0] with probability 0. 95, with a marginal log Cauchy ? 2 distribution, to obtain the gamma prior ? v ? Ga(0. 5, 0. 00149).The term exp(u k ) reflects the smooth component of the residual relative risk, and the specification of a 2 prior for the associated variance component ? u is more difficult, given its conditional interpretation. Using the algorithm described in Section 4. 2, we examined simulations of u for different choices of gamma ? 2 hyperparameters and decided on the choice ? u ? Ga(0. 5, 0. 001); Figure 2 shows 10 realizations from the prior. The rationale here is to examine realizations to see if they conform to our prior expectations and in particular exhibit the required amount of smoothing.All but one of the realizations vary smoothly across the 11 cohorts, as is desirable. Due to the tail of the gamma distribution, we will always have some extreme realizations. The INLA results, summarized in graphical form, are presented in Figure 2(b), alongside likelihood fits in which the birth cohort effect is incorporated as a linear term and as a f actor. We see that the smoothing model provides a smooth fit in birth cohort, as we would hope. 5. 3 B-Spline nonparametric regression We demonstrate the use of INLA for nonparametric smoothing using O’Sullivan splines, which are based on a B-spline basis.We illustrate using data from Bachrach and others (1999) that concerns longitudinal measurements of spinal bone mineral density (SBMD) on 230 female subjects aged between 8 and 27, and of 1 of 4 ethnic groups: Asian, Black, Hispanic, and White. Let yi j denote the SBMD measure for subject i at occasion j, for i = 1, . . . , 230 and j = 1, . . . , n i with n i being between 1 and 4. Figure 3 shows these data, with the gray lines indicating measurements on the same woman. We assume the model K Yi j = x i ? 1 + agei j ? 2 + k=1 z i jk b1k + b2i + ij, where x i is a 1 ? vector containing an indicator for the ethnicity of individual i, with ? 1 the associated 4 ? 1 vector of fixed effects, z i jk is the kth basis associated with age, with associated parameter b1k ? 2 2 N (0, ? 1 ), and b2i ? N (0, ? 2 ) are woman-specific random effects, finally, i j ? iid N (0, ? 2 ). All random terms are assumed independent. Note that the spline model is assumed common to all ethnic groups and all women, though it would be straightforward to allow a different spline for each ethnicity. Writing this model in the form y = x ? + z 1b1 + z 2b 2 + = C ? + . Bayesian GLMMs 407Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 Fig. 2. (a) Ten realizations (on the relative risk scale) from the random effects second-order random walk model in which the prior on the random-effects precision is Ga(0. 5,0. 001), (b) summaries of fitted models: the solid line corresponds to a log-linear model in birth cohort, the circles to birth cohort as a factor, and â€Å"+† to the Bayesian smoothing model. we use the method described in Section 4. 3 to examine the effective number of parameters implied by the ? 2 ? 2 priors ? 1 ? Ga(a1 , a2 ) and ? 2 ? Ga(a3 , a4 ).To fit the model, we first use the R code provided in Wand and Ormerod (2008) to construct the basis functions, which are then input to the INLA program. Running the REML version of the model, we obtain 2 ? = 0. 033 which we use to evaluate the effective degrees of freedoms associated with priors for ? 1 and 2 . We assume the usual improper prior, ? (? 2 ) ? 1/? 2 for ? 2 . After some experimentation, we settled ? 2 408 Y. F ONG AND OTHERS Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 Fig. 3. SBMD versus age by ethnicity. Measurements on the same woman are joined with gray lines.The solid curve corresponds to the fitted spline and the dashed lines to the individual fits. ?2 2 on the prior ? 1 ? Ga(0. 5, 5 ? 10? 6 ). For ? 2 , we wished to have a 90% interval for b2i of  ±0. 3 which, ? 2 with 1 degree of freedom for the marginal distributio n, leads to ? 2 ? Ga(0. 5, 0. 00113). Figure 4 shows the priors for ? 1 and ? 2 , along with the implied effective degrees of freedom under the assumed priors. For the spline component, the 90% prior interval for the effective degrees of freedom is [2. 4,10]. Table 2 compares estimates from REML and INLA implementations of the model, and we see close correspondence between the 2.Figure 4 also shows the posterior medians for ? 1 and ? 2 and for the 2 effective degrees of freedom. For the spline and random effects these correspond to 8 and 214, respectively. The latter figure shows that there is considerable variability between the 230 women here. This is confirmed in Figure 3 where we observe large vertical differences between the profiles. This figure also shows the fitted spline, which appears to mimic the trend in the data well. 5. 4 Timings For the 3 models in the longitudinal data example, INLA takes 1 to 2 s to run, using a single CPU.To get estimates with similar precision wit h MCMC, we ran JAGS for 100 000 iterations, which took 4 to 6 min. For the model in the temporal smoothing example, INLA takes 45 s to run, using 1 CPU. Part of the INLA procedure can be executed in a parallel manner. If there are 2 CPUs available, as is the case with today’s prevalent INTEL Core 2 Duo processors, INLA only takes 27 s to run. It is not currently possible to implement this model in JAGS. We ran the MCMC utility built into the INLA software for 3. 6 million iterations, to obtain estimates of comparable accuracy, which took 15 h.For the model in the B-spline nonparametric regression example, INLA took 5 s to run, using a single CPU. We ran the MCMC utility built into the INLA software for 2. 5 million iterations to obtain estimates of comparable accuracy, the analysis taking 40 h. Bayesian GLMMs 409 Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 Fig. 4. Prior summaries: (a) ? 1 , the standard deviation of the spline coefficients, (b) effective degrees of freedom associated with the prior for the spline coefficients, (c) effective degrees of freedom versus ? , (d) ? 2 , the standard deviation of the between-individual random effects, (e) effective degrees of freedom associated with the individual random effects, and (f) effective degrees of freedom versus ? 2 . The vertical dashed lines on panels (a), (b), (d), and (e) correspond to the posterior medians. Table 2. REML and INLA summaries for spinal bone data. Intercept corresponds to Asian group Variable Intercept Black Hispanic White Age ? 1 ? 2 ? REML 0. 560  ± 0. 029 0. 106  ± 0. 021 0. 013  ± 0. 022 0. 026  ± 0. 022 0. 021  ± 0. 002 0. 018 0. 109 0. 033 INLA 0. 563  ± 0. 031 0. 106  ± 0. 021 0. 13  ± 0. 022 0. 026  ± 0. 022 0. 021  ± 0. 002 0. 024  ± 0. 006 0. 109  ± 0. 006 0. 033  ± 0. 002 Note: For the entries marked with a standard errors were unavailable. 410 Y. F ONG AND OTHERS 6. D ISCUSSION In t his paper, we have demonstrated the use of the INLA computational method for GLMMs. We have found that the approximation strategy employed by INLA is accurate in general, but less accurate for binomial data with small denominators. The supplementary material available at Biostatistics online contains an extensive simulation study, replicating that presented in Breslow and Clayton (1993).There are some suggestions in the discussion of Rue and others (2009) on how to construct an improved Gaussian approximation that does not use the mode and the curvature at the mode. It is likely that these suggestions will improve the results for binomial data with small denominators. There is an urgent need for diagnosis tools to flag when INLA is inaccurate. Conceptually, computation for nonlinear mixed effects models (Davidian and Giltinan, 1995; Pinheiro and Bates, 2000) can also be handled by INLA but this capability is not currently available. The website www. r-inla. rg contains all the data and R scripts to perform the analyses and simulations reported in the paper. The latest release of software to implement INLA can also be found at this site. Recently, Breslow (2005) revisited PQL and concluded that, â€Å"PQL still performs remarkably well in comparison with more elaborate procedures in many practical situations. † We believe that INLA provides an attractive alternative to PQL for GLMMs, and we hope that this paper stimulates the greater use of Bayesian methods for this class. Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013S UPPLEMENTARY MATERIAL Supplementary material is available at http://biostatistics. oxfordjournals. org. ACKNOWLEDGMENT Conflict of Interest: None declared. F UNDING National Institutes of Health (R01 CA095994) to J. W. Statistics for Innovation (sfi. nr. no) to H. R. R EFERENCES BACHRACH , L. K. , H ASTIE , T. , WANG , M. C. , NARASIMHAN , B. AND M ARCUS , R. (1999). Bone mineral acquisition in healthy Asian, Hispanic, Black and Caucasian youth. A longitudinal study. The Journal of Clinical Endocrinology and Metabolism 84, 4702–4712. 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