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Informationen zum Autor Clair Alston, Queensland University of Technology and Science, Australia. Kerrie L. Mengersen, Queensland University of Technology and Science, Australia. Tony Pettitt, Queensland University of Technology and Science, Australia. Klappentext Provides an accessible foundation to Bayesian analysis using real world modelsThis book aims to present an introduction to Bayesian modelling and computation, by considering real case studies drawn from diverse fields spanning ecology, health, genetics and finance. Each chapter comprises 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.Case Studies in Bayesian Statistical Modelling and Analysis:* Illustrates how to do Bayesian analysis in a clear and concise manner using real-world problems.* Each chapter focuses on a real-world problem and describes the way in which the problem may be analysed using Bayesian methods.* Features approaches that can be used in a wide area of application, such as, health, the environment, genetics, information science, medicine, biology, industry and remote sensing.Case Studies in Bayesian Statistical Modelling and Analysis is aimed at statisticians, researchers and practitioners who have some expertise in statistical modelling and analysis, and some understanding of the basics of Bayesian statistics, but little experience in its application. Graduate students of statistics and biostatistics will also find this book beneficial. Zusammenfassung Provides an accessible foundation to Bayesian analysis using real world models This book aims to present an introduction to Bayesian modelling and computation, by considering real case studies drawn from diverse fields spanning ecology, health, genetics and finance. Inhaltsverzeichnis 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 1.3.1 Bayesian theory and methodology 8 1.3.2 Bayesian methodology 10 1.3.3 Bayesian computation 10 1.3.4 Bayesian software 11 1.3.5 Applications 13 References 13 2 Introduction to MCMC 17 Anthony N. Pettitt and Candice M. Hincksman 2.1 Introduction 17 2.2 Gibbs sampling 18 2.2.1 Example: Bivariate normal 18 2.2.2 Example: Change-point model 19 2.3 Metropolis-Hastings algorithms 19 2.3.1 Example: Component-wise MH or MH within Gibbs 20 2.3.2 Extensions to basic MCMC 21 2.3.3 Adaptive MCMC 22 2.3.4 Doubly intractable problems 22 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 3.1.1 Priors as a basis for learning 32 3.1.2 Priors and philosophy 32 3.1.3 Prior chronology 33 3.1.4 Pooling prior information 34 3.2 Methodology I: Priors defined by mathematical criteria 35 3.2.1 Conjugate priors 35 3.2.2 Impropriety and hierarchical priors 37 3.2.3 Zellner's g-prior for regression models 37 3.2.4 Objective priors 38 3.3 Methodology II: Modelling informative priors 40 3.3.1 Informative modelling approaches 40 3.3.2 Elicitation of distributions 42 3.4 Case studies 44 3.4.1 Normal likelihood: Time to submit research dissertations 44 3.4.2 Binomial likelihood: Surveillance for exotic plant pests 47 3.4.3 Mixture model likelihood: Bioregionalization 50 3.4.4 Logistic regression likelihood: Mapping species distr...
List of contents
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
1.3.1 Bayesian theory and methodology 8
1.3.2 Bayesian methodology 10
1.3.3 Bayesian computation 10
1.3.4 Bayesian software 11
1.3.5 Applications 13
References 13
2 Introduction to MCMC 17
Anthony N. Pettitt and Candice M. Hincksman
2.1 Introduction 17
2.2 Gibbs sampling 18
2.2.1 Example: Bivariate normal 18
2.2.2 Example: Change-point model 19
2.3 Metropolis-Hastings algorithms 19
2.3.1 Example: Component-wise MH or MH within Gibbs 20
2.3.2 Extensions to basic MCMC 21
2.3.3 Adaptive MCMC 22
2.3.4 Doubly intractable problems 22
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
3.1.1 Priors as a basis for learning 32
3.1.2 Priors and philosophy 32
3.1.3 Prior chronology 33
3.1.4 Pooling prior information 34
3.2 Methodology I: Priors defined by mathematical criteria 35
3.2.1 Conjugate priors 35
3.2.2 Impropriety and hierarchical priors 37
3.2.3 Zellner's g-prior for regression models 37
3.2.4 Objective priors 38
3.3 Methodology II: Modelling informative priors 40
3.3.1 Informative modelling approaches 40
3.3.2 Elicitation of distributions 42
3.4 Case studies 44
3.4.1 Normal likelihood: Time to submit research dissertations 44
3.4.2 Binomial likelihood: Surveillance for exotic plant pests 47
3.4.3 Mixture model likelihood: Bioregionalization 50
3.4.4 Logistic regression likelihood: Mapping species distribution via habitat models 53
3.5 Discussion 57
3.5.1 Limitations 57
3.5.2 Finding out about the problem 58
3.5.3 Prior formulation 59
3.5.4 Communication 60
3.5.5 Conclusion 61
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
4.2.1 Case study 1: Boston housing data set 67
4.2.2 Case study 2: Production of cars and station wagons 67
4.3 Matrix notation and the likelihood 67
4.4 Posterior inference 68
4.4.1 Natural conjugate prior 69
4.4.2 Alternative prior specifications 73
4.4.3 Generalizations of the normal linear model 74
4.4.4 Variable selection 78
4.5 Analysis 81
4.5.1 Case study 1: Boston housing data set 81
4.5.2 Case study 2: Car production data set 85
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
5.4.1 Updating using the training data 96
5.4.2 Updating the model yearly 98
5.5 Discussion 100
References 101
6 A Bayesian regression model with variable selection for genome-wide association
