Jonathan Homola, Hong Min Park Je Gill

Jonathan Homola, Hong Min Park & Je Gill

Bayesian Methods: A

Social and Behavioral Sciences Approach,

ANSWER KEY

THIRDEDITION

September 2016 (Solutions Manual All Chapters, 100% Original Verified, A+ Grade) 1 / 4

Contents

• Background and Introduction 1
• Specifying Bayesian Models 11
• The Normal and Student's-t Models 23
• The Bayesian Prior 39
• The Bayesian Linear Model 53
• Assessing Model Quality 71
• Bayesian Hypothesis Testing and the Bayes Factor 89
• Monte Carlo Methods 101
• Basics of Markov Chain Monte Carlo 119

10 Bayesian Hierarchical Models 137 11 Some Markov Chain Monte Carlo Theory 153 12 Utilitarian Markov Chain Monte Carlo 163 A Generalized Linear Model Review 191 vii 2 / 4

List of Tables 1.1 Posteriors from Dierent Priors . . . . . . . . . . . . . . . . . .9 2.1 HPD w/ Dierent Values . . . . . . . . . . . . . . . . . . . . .20 3.1 Posterior of the bivariate model . . . . . . . . . . . . . . . . . .36 4.1 Summary Statistics of's . . . . . . . . . . . . . . . . . . . . .51 5.1 Posteriors of Meier and Keiser (1996) model . . . . . . . . . . .58 5.2 Posteriors of Alcohol vs. Tobacco model . . . . . . . . . . . . .62 5.3 Posteriors of Ancient China Conict Model . . . . . . . . . . .67 6.1 Robustness measurejjD(q)jj. . . . . . . . . . . . . . . . . . . .78 6.2 Posterior predictive distributions from two priors . . . . . . . .82 12.1 Geweke's Diagnostics from Dierent Sources . . . . . . . . . . .170 12.2 Geweke versus Gelman-Rubin . . . . . . . . . . . . . . . . . . .179 12.3 Unconditional vs. Rao-Blackwellized Posteriors . . . . . . . . .182 A.1 Three Dierent Binomial Models . . . . . . . . . . . . . . . . .200ix 3 / 4

List of Figures 1.1 Plots of marginal distributions for dierent values ofBandm.3 1.2 Plots of the marginal distributions ofxandyfor dierent can- didate generating distributions. . . . . . . . . . . . . . . . . . .6 2.1 The Posterior Density ofp(jy) with Dierent Priors . . . . . .12 2.2 Posterior distribution of. . . . . . . . . . . . . . . . . . . . . .15 3.1 Relative Importance of Likelihood to Prior . . . . . . . . . . . .27 3.2 Cauchy distribution with Normal's . . . . . . . . . . . . . . . .29 5.1 Plot of posteriorusing jackkning . . . . . . . . . . . . . . .56 5.2 Posteriors of Meier and Keiser (1996) model . . . . . . . . . . .58 5.3 Model t for Ancient China Conict Model . . . . . . . . . . .68 6.1 Polasek Diagnostic for Meier and Keiser (1996) model . . . . .75 6.2 Exponential Model Sensitivity . . . . . . . . . . . . . . . . . . .77 6.3 Posteriors forand 2 w/ dierent priors . . . . . . . . . . .79 6.4 Posterior distributions of mu from two priors . . . . . . . . . .83

8.1 Drawing Beta Distribution: Johnk's Method vs.rbeta. . . . .

115 9.1 Mean recurrence time with respect to p . . . . . . . . . . . . .134 10.1 Traceplots for One-Way Random Eects Model . . . . . . . . .144 12.1 Dierent Annealing Cooling Schedules . . . . . . . . . . . . . .167 A.1 Contour Plot of Bivariate Normal Distribution . . . . . . . . .194 A.2 Finding Inuential Outliers . . . . . . . . . . . . . . . . . . . .196xi

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