Bayesian Computation with R

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Springer Science & Business Media, 2007 - Computers - 267 pages
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There has been a dramatic growth in the development and application of Bayesian inferential methods. Some of this growth is due to the availability of powerful simulation-based algorithms to summarize posterior distributions. There has been also a growing interest in the use of the system R for statistical analyses. R's open source nature, free availability, and large number of contributor packages have made R the software of choice for many statisticians in education and industry.

Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language. The early chapters present the basic tenets of Bayesian thinking by use of familiar one and two-parameter inferential problems. Bayesian computational methods such as Laplace's method, rejection sampling, and the SIR algorithm are illustrated in the context of a random effects model. The construction and implementation of Markov Chain Monte Carlo (MCMC) methods is introduced. These simulation-based algorithms are implemented for a variety of Bayesian applications such as normal and binary response regression, hierarchical modeling, order-restricted inference, and robust modeling. Algorithms written in R are used to develop Bayesian tests and assess Bayesian models by use of the posterior predictive distribution. The use of R to interface with WinBUGS, a popular MCMC computing language, is described with several illustrative examples.

This book is a suitable companion book for an introductory course on Bayesian methods and is valuable to the statistical practitioner who wishes to learn more about the R language and Bayesian methodology. The LearnBayes package, written by the author and available from the CRAN website, contains all of the R functions described in the book.

The second edition contains several new topics such as the use of mixtures of conjugate priors and the use of Zellnera (TM)s g priors to choose between models in linear regression. There are more illustrations of the construction of informative prior distributions, such as the use of conditional means priors and multivariate normal priors in binary regressions. The new edition contains changes in the R code illustrations according to the latest edition of the LearnBayes package.

 

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Contents

An Introduction to R
1
122 Reading the Data into R
2
124 R Commands to Compare Batches
4
125 R Commands for Studying Relationships
6
13 Exploring the Robustness of the t Statistic
8
132 Writing a Function to Compute the t Statistic
9
133 Programming a Monte Carlo Simulation
11
134 The Behavior of the True Significance Level Under Different Assumptions
12
613 Exercises
131
Hierarchical Modeling
136
73 Individual and Combined Estimates
139
74 Equal Mortality Rates?
141
75 Modeling a Prior Belief of Exchangeability
145
76 Posterior Distribution
147
78 Posterior Inferences
151
781 Shrinkage
152

14 Further Reading
13
15 Summary of R Functions
14
16 Exercises
15
Introduction to Bayesian Thinking
19
23 Using a Discrete Prior
20
24 Using a Beta Prior
22
25 Using a Histogram Prior
26
26 Prediction
29
27 Further Reading
34
29 Exercises
35
SingleParameter Models
38
33 Estimating a Heart Transplant Mortality Rate
41
34 An Illustration of Bayesian Robustness
44
35 A Bayesian Test of the Fairness of a Coin
50
36 Further Reading
53
38 Exercises
54
Multiparameter Models
57
43 A Multinomial Model
60
45 Comparing Two Proportions
65
46 Further Reading
70
48 Exercises
71
Introduction to Bayesian Computation
75
52 Computing Integrals
76
53 Setting Up a Problem on R
77
54 A BetaBinomial Model for Overdispersion
78
55 Approximations Based on Posterior Modes
80
56 The Example
82
57 Monte Carlo Method for Computing Integrals
84
58 Rejection Sampling
85
59 Importance Sampling
88
510 Sampling Importance Resampling
91
511 Further Reading
94
513 Exercises
96
Markov Chain Monte Carlo Methods
101
63 MetropolisHasting Algorithms
104
64 Gibbs Sampling
106
66 A Strategy in Bayesian Computing
108
68 Example of Output Analysis
113
69 Modeling Data with Cauchy Errors
116
610 Analysis of the Stanford Heart Transplant Data
124
611 Further Reading
129
612 Summary of R Functions
130
782 Comparing Hospitals
153
79 Posterior Predictive Model Checking
155
710 Further Reading
157
711 Summary of R Functions
158
Model Comparison
163
83 A OneSided Test of a Normal Mean
164
84 A TwoSided Test of a Normal Mean
167
85 Comparing Two Models
168
86 Models for Soccer Goals
169
87 Is a Baseball Hitter Really Streaky?
172
88 A Test of Independence in a TwoWay Contingency Table
176
89 Further Reading
180
810 Summary of R Functions
181
811 Exercises
183
Regression Models
186
922 The Posterior Distribution
188
924 Computation
189
926 An Example
190
93 Survival Modeling
199
94 Further Reading
204
95 Summary of R Functions
205
96 Exercises
206
Gibbs Sampling
211
102 Robust Modeling
212
103 Binary Response Regression with a Probit Link
216
104 Estimating a Table of Means
219
1042 A Flat Prior Over the Restricted Space
223
1043 A Hierarchical Regression Prior
227
1044 Predicting the Success of Future Students
232
105 Further Reading
233
107 Exercises
234
Using R to Interface with WinBUGS
237
112 An R Interface to WinBUGS
238
113 MCMC Diagnostics Using the boa Package
239
114 A ChangePoint Model
240
115 A Robust Regression Model
243
116 Estimating Career Trajectories
247
117 Further Reading
253
118 Exercises
254
References
259
Index
263
Copyright

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Page 261 - Different chemotherapeutic sensitivities and host factors affecting prognosis in advanced ovarian carcinoma versus minimal residual disease.
Page 260 - Fitting and checking a two-level Poisson model: modeling patient mortality rates in heart transplant patients,
Page 261 - Journal of the American Statistical Association, 85, 972-985. Gelman, A., Carlin, J., Stern, H. and Rubin, D. (2003), Bayesian Data Analysis, New York: Chapman and Hall. Gelman, A., Meng, X. and Stern, H. (1996), "Posterior predictive assessment of model fitness via realized discrepancies," Statistics Sinica, 6, 733-807.
Page 259 - A Bayesian analysis of a Poisson random effects model for home run hitters," The American Statistician, 46, 246-253.

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About the author (2007)

Jim Albert is Professor of Statisitics at Bowling Green State University.

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