|  | Alston, Clair L. / Mengersen, Kerrie L. / Pettitt, Anthony N. (Hrsg.)
Case Studies in Bayesian Statistical Modelling and Analysis
Wiley Series in Probability and Statistics
 1. Auflage November 2012
83,90 Euro
2012. 598 Seiten, Hardcover
ISBN 978-1-119-94182-8 - John Wiley & Sons
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Case Studies in Bayesian Statistical Modelling and Analysis provides an accessible foundation into Bayesian modelling and analysis using real-world models. Each chapter comprises of a description of the problem, the corresponding model, the computational method, results, and inferences as well as the issues that arise in the implementation of these approaches. Coverage focuses on a real-world problems drawn from the editors' own experiences while illustrating the way in which the problem can be analyzed using Bayesian methods.
Aus dem Inhalt
Preface xvii
List of contributors xix
1 Introduction 1
Clair L. Alston, Margaret Donald, Kerrie L. Mengersen and Anthony N. Pettitt
1.1 Introduction 1
1.2 Overview 1
1.3 Further reading 8
References 13
2 Introduction to MCMC 17
Anthony N. Pettitt and Candice M. Hincksman
2.1 Introduction 17
2.2 Gibbs sampling 18
2.3 Metropolis-Hastings algorithms 19
2.4 Approximate Bayesian computation 24
2.5 Reversible jump MCMC 25
2.6 MCMC for some further applications 26
References 27
3 Priors: Silent or active partners of Bayesian inference? 30
Samantha Low Choy
3.1 Priors in the very beginning 30
3.2 Methodology I: Priors defined by mathematical criteria 35
3.3 Methodology II: Modelling informative priors 40
3.4 Case studies 44
3.5 Discussion 57
Acknowledgements 61
References 61
4 Bayesian analysis of the normal linear regression model 66
Christopher M. Strickland and Clair L. Alston
4.1 Introduction 66
4.2 Case studies 67
4.3 Matrix notation and the likelihood 67
4.4 Posterior inference 68
4.5 Analysis 81
References 88
5 Adapting ICU mortality models for local data: A Bayesian approach 90
Petra L. Graham, Kerrie L. Mengersen and David A. Cook
5.1 Introduction 90
5.2 Case study: Updating a known risk-adjustment model for local use 91
5.3 Models and methods 92
5.4 Data analysis and results 96
5.5 Discussion 100
References 101
6 A Bayesian regression model with variable selection for genome-wide association studies 103
Carla Chen, Kerrie L. Mengersen, Katja Ickstadt and Jonathan M. Keith
6.1 Introduction 103
6.2 Case study: Case-control of Type 1 diabetes 104
6.3 Case study: GENICA 105
6.4 Models and methods 105
6.5 Data analysis and results 109
6.6 Discussion 112
Acknowledgements 115
References 115
6.A Appendix: SNP IDs 117
7 Bayesian meta-analysis 118
Jegar O. Pitchforth and Kerrie L. Mengersen
7.1 Introduction 118
7.2 Case study 1: Association between red meat consumption and breast cancer 119
7.3 Case study 2: Trends in fish growth rate and size 130
Acknowledgements 137
References 138
8 Bayesian mixed effects models 141
Clair L. Alston, Christopher M. Strickland, Kerrie L. Mengersen and Graham E. Gardner
8.1 Introduction 141
8.2 Case studies 142
8.3 Models and methods 146
8.4 Data analysis and results 150
8.5 Discussion 158
References 158
9 Ordering of hierarchies in hierarchical models: Bone mineral density estimation 159
Cathal D. Walsh and Kerrie L. Mengersen
9.1 Introduction 159
9.2 Case study 160
9.3 Models 161
9.4 Data analysis and results 164
9.5 Discussion 168
References 168
9.A Appendix: Likelihoods 170
10 BayesianWeibull survival model for gene expression data 171
Sri Astuti Thamrin, James M. McGree and Kerrie L. Mengersen
10.1 Introduction 171
10.2 Survival analysis 172
10.3 Bayesian inference for the Weibull survival model 174
10.4 Case study 178
10.5 Discussion 182
References 183
11 Bayesian change point detection in monitoring clinical outcomes 186
Hassan Assareh, Ian Smith and Kerrie L. Mengersen
11.1 Introduction 186
11.2 Case study: Monitoring intensive care unit outcomes 187
11.3 Risk-adjusted control charts 187
11.4 Change point model 188
11.5 Evaluation 189
11.6 Performance analysis 190
11.7 Comparison of Bayesian estimator with other methods 194
11.8 Conclusion 194
References 195
12 Bayesian splines 197
Samuel Clifford and Samantha Low Choy
12.1 Introduction 197
12.2 Models and methods 197
12.3 Case studies 207
12.4 Conclusion 216
References 218
13 Disease mapping using Bayesian hierarchical models 221
Arul Earnest, Susanna M. Cramb and Nicole M. White
13.1 Introduction 221
13.2 Case studies 224
13.3 Models and methods 225
13.4 Data analysis and results 230
13.5 Discussion 234
References 237
14 Moisture, crops and salination: An analysis of a three-dimensional agricultural data set 240
Margaret Donald, Clair L. Alston, Rick Young and Kerrie L. Mengersen
14.1 Introduction 240
14.2 Case study 241
14.3 Review 243
14.4 Case study modelling 243
14.5 Model implementation: Coding considerations 246
14.6 Case study results 247
14.7 Conclusions 249
References 250
15 A Bayesian approach to multivariate state space modelling: A study of a Fama-French asset-pricing model with time-varying regressors 252
Christopher M. Strickland and Philip Gharghori
15.1 Introduction 252
15.2 Case study: Asset pricing in financial markets 253
15.3 Time-varying Fama-French model 254
15.4 Bayesian estimation 256
15.5 Analysis 261
15.6 Conclusion 264
References 265
16 Bayesian mixture models: When the thing you need to know is the thing you cannot measure 267
Clair L. Alston, Kerrie L. Mengersen and Graham E. Gardner
16.1 Introduction 267
16.2 Case study: CT scan images of sheep 268
16.3 Models and methods 270
16.4 Data analysis and results 276
16.5 Discussion 284
References 284
17 Latent class models in medicine 287
Margaret Rolfe, Nicole M. White and Carla Chen
17.1 Introduction 287
17.2 Case studies 288
17.3 Models and methods 289
17.4 Data analysis and results 300
17.5 Discussion 306
References 307
18 Hidden Markov models for complex stochastic processes: A case study in electrophysiology 310
Nicole M. White, Helen Johnson, Peter Silburn, Judith Rousseau and Kerrie L. Mengersen
18.1 Introduction 310
18.2 Case study: Spike identification and sorting of extracellular recordings 311
18.3 Models and methods 312
18.4 Data analysis and results 320
18.5 Discussion 326
References 327
19 Bayesian classification and regression trees 330
Rebecca A. O'Leary, Samantha Low Choy, Wenbiao Hu and Kerrie L. Mengersen
19.1 Introduction 330
19.2 Case studies 332
19.3 Models and methods 334
19.4 Computation 337
19.5 Case studies - results 341
19.6 Discussion 345
References 346
20 Tangled webs: Using Bayesian networks in the fight against infection 348
Mary Waterhouse and Sandra Johnson
20.1 Introduction to Bayesian network modelling 348
20.2 Introduction to case study 351
20.3 Model 352
20.4 Methods 354
20.5 Results 355
20.6 Discussion 357
References 359
21 Implementing adaptive dose finding studies using sequential Monte Carlo 361
James M. McGree, Christopher C. Drovandi and Anthony N. Pettitt
21.1 Introduction 361
21.2 Model and priors 363
21.3 SMC for dose finding studies 364
21.4 Example 369
21.5 Discussion 371
References 372
21.A Appendix: Extra example 373
22 Likelihood-free inference for transmission rates of nosocomial pathogens 374
Christopher C. Drovandi and Anthony N. Pettitt
22.1 Introduction 374
22.2 Case study: Estimating transmission rates of nosocomial pathogens 375
22.3 Models and methods 376
22.4 Data analysis and results 384
22.5 Discussion 385
References 386
23 Variational Bayesian inference for mixture models 388
Clare A. McGrory
23.1 Introduction 388
23.2 Case study: Computed tomography (CT) scanning of a loin portion of a pork carcase 390
23.3 Models and methods 392
23.4 Data analysis and results 397
23.5 Discussion 399
References 399
23.A Appendix: Form of the variational posterior for a mixture of multivariate normal densities 401
24 Issues in designing hybrid algorithms 403
Jeong E. Lee, Kerrie L. Mengersen and Christian P. Robert
24.1 Introduction 403
24.2 Algorithms and hybrid approaches 406
24.3 Illustration of hybrid algorithms 412
24.4 Discussion 417
References 418
25 A Python package for Bayesian estimation using Markov chain Monte Carlo 421
Christopher M. Strickland, Robert J. Denham, Clair L. Alston and Kerrie L. Mengersen
25.1 Introduction 421
25.2 Bayesian analysis 423
25.3 Empirical illustrations 437
25.4 Using PyMCMC efficiently 451
25.5 PyMCMC interacting with R 457
25.6 Conclusions 458
25.7 Obtaining PyMCMC 459
References 459
Index 461
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