• Paperback: 270 pages
• Publisher: Springer; 1st ed. 2007. Corr. 2nd printing edition (June 11, 2008)
• Language: English
• ISBN-10: 0387713840
• ISBN-13: 978-0387713847

Contents
1 An Introduction to R 1
1.1 Overview 1
1.2 Exploring a Student Dataset 1
1.2.1 Introduction to the Dataset 1
1.2.2 Reading the Data into R 2
1.2.3 R Commands to Summarize and Graph a Single Batch
2
1.2.4 R Commands to Compare Batches 5
1.2.5 R Commands for Studying Relationships 6
1.3 Exploring the Robustness of the t Statistic 8
1.3.1 Introduction 8
1.3.2 Writing a Function to Compute the t Statistic 9
1.3.3 Programming a Monte Carlo Simulation 10
1.3.4 The Behavior of the True Significance Level Under Different Assumptions .11
1.4 Further Reading13
1.5 Summary of R Functions 14
1.6 Exercises 15
2 Introduction to Bayesian Thinking 19
2.1 Introduction 19
2.2 Learning About the Proportion of Heavy Sleepers 19
2.3 Using a Discrete Prior 20
2.4 Using a Beta Prior 22
2.5 Using a Histogram Prior 26
2.6 Prediction 28
2.7 Further Reading34
2.8 Summary of R Functions 34
2.9 Exercises 35

3 Single-Parameter Models 39
3.1 Introduction 39
3.2 Normal Distribution with Known Mean but Unknown Variance .39
3.3 Estimating a Heart Transplant Mortality Rate 41
3.4 An Illustration of Bayesian Robustness 44
3.5 Mixtures of Conjugate Priors 49
3.6 A Bayesian Test of the Fairness of a Coin52
3.7 Further Reading57
3.8 Summary of R Functions 57
3.9 Exercises 58
4 Multiparameter Models 63
4.1 Introduction 63
4.2 Normal Data with Both Parameters Unknown 63
4.3 A Multinomial Model 66
4.4 A Bioassay Experiment 69
4.5 Comparing Two Proportions 75
4.6 Further Reading80
4.7 Summary of R Functions 80
4.8 Exercises 81
5 Introduction to Bayesian Computation 87
5.1 Introduction 87
5.2 Computing Integrals 88
5.3 Setting Up a Problem in R 89
5.4 A Beta-Binomial Model for Overdispersion 90
5.5 Approximations Based on Posterior Modes 94
5.6 The Example 95
5.7 Monte Carlo Method for Computing Integrals 97
5.8 Rejection Sampling 98
5.9 Importance Sampling 101
5.9.1 Introduction 101
5.9.2 Using a Multivariate t as a Proposal Density 103
5.10 Sampling Importance Resampling 105
5.11 Further Reading 108
5.12 Summary of R Functions 109
5.13 Exercises 110
6 Markov Chain Monte Carlo Methods 117
6.1 Introduction 117
6.2 Introduction to Discrete Markov Chains 117
6.3 Metropolis-Hastings Algorithms 120
6.4 Gibbs Sampling 122
6.5 MCMC Output Analysis 122

6.6 A Strategy in Bayesian Computing 124
6.7 Learning About a Normal Population from Grouped Data 124
6.8 Example of Output Analysis 129
6.9 Modeling Data with Cauchy Errors 131
6.10 Analysis of the Stanford Heart Transplant Data 140
6.11 Further Reading 145
6.12 Summary of R Functions 146
6.13 Exercises 147
7 Hierarchical Modeling 153
7.1 Introduction 153
7.2 Three Examples 153
7.3 Individual and Combined Estimates 155
7.4 Equal Mortality Rates? 157
7.5 Modeling a Prior Belief of Exchangeability 161
7.6 Posterior Distribution 163
7.7 Simulating from the Posterior 163
7.8 Posterior Inferences 168
7.8.1 Shrinkage 168
7.8.2 Comparing Hospitals 169
7.9 Bayesian Sensitivity Analysis 171
7.10 Posterior Predictive Model Checking 173
7.11 Further Reading 175
7.12 Summary of R Functions 175
7.13 Exercises 176
8 Model Comparison 181
8.1 Introduction 181
8.2 Comparison of Hypotheses 181
8.3 A One-Sided Test of a Normal Mean 182
8.4 A Two-Sided Test of a Normal Mean 185
8.5 Comparing Two Models 186
8.6 Models for Soccer Goals 187
8.7 Is a Baseball Hitter Really Streaky? 190
8.8 A Test of Independence in a Two-Way Contingency Table 194
8.9 Further Reading199
8.10 Summary of R Functions 199
8.11 Exercises 201
9 Regression Models  205
9.1 Introduction 205
9.2 Normal Linear Regression 205
9.2.1 The Model 205
9.2.2 The Posterior Distribution 206
9.2.3 Prediction of Future Observations 206

9.2.4 Computation 207
9.2.5 Model Checking 207
9.2.6 An Example 208
9.3 Model Selection Using Zellner’s g Prior 217
9.4 Survival Modeling 222
9.5 Further Reading227
9.6 Summary of R Functions 227
9.7 Exercises 229
10 Gibbs Sampling 235
10.1 Introduction 235
10.2 Robust Modeling 236
10.3 Binary Response Regression with a Probit Link 240
10.3.1 Missing Data and Gibbs Sampling 240
10.3.2 Proper Priors and Model Selection 243
10.4 Estimating a Table of Means 248
10.4.1 Introduction 248
10.4.2 A Flat Prior Over the Restricted Space 250
10.4.3 A Hierarchical Regression Prior 254
10.4.4 Predicting the Success of Future Students 259
10.5 Further Reading 260
10.6 Summary of R Functions 260
10.7 Exercises 261
11 Using R to Interface with WinBUGS 265
11.1 Introduction to WinBUGS 265
11.2 An R Interface to WinBUGS 266
11.3 MCMC Diagnostics Using the coda Package 267
11.4 A Change-Point Model 268
11.5 A Robust Regression Model 272
11.6 Estimating Career Trajectories 276
11.7 Further Reading 281
11.8 Exercises 282
References  287
Index  293