Case studies in Bayesian statistical modelling and analysis

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. 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.

Author Notes

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.

List of Contributors
Contributors
Preface
1 IntroductionClair Alston and Margaret Donald and Kerrie Mengersen and Anthony Pettitt
1.1 Introduction
1.2 Overview
1.3 Further Reading
1.3.1 Bayesian theory and methodology
1.3.2 Bayesian Theory and Methodology
1.3.3 Bayesian Computation
1.3.4 Bayesian Software
1.3.5 Applications
References
2 Introduction to MCMCAnthony N. Pettitt and Candice M. Hincksman
2.1 Introduction
2.2 Gibbs Sampling
2.2.1 Example: Bivariate normal
2.2.2 Example: Change point model
2.3 Metropolis-Hastings algorithms
2.3.1 Example: Component wise MH or MH within Gibbs
2.3.2 Extensions to basic MCMC
2.3.3 Adaptive MCMC
2.3.4 Doubly intractable problem
2.4 Approximate Bayesian Computation (ABC)
2.5 Reversible Jump Markov chain Monte Carlo
2.6 MCMC for some further applications
References
3 Priors: Silent or Active Partners of Bayesian Inference?Samantha Low-Choy
3.1 Priors in the very beginning
3.1.1 Priors as a basis for Learning
3.1.2 Priors and Philosophy
3.1.3 Prior chronology
3.1.4 Pooling Prior Information
3.2 Methodology I: Priors defined by mathematical criteria
3.2.1 Conjugate Priors
3.2.2 Conjugacy for a Normal prior on the mean, in a Normal likelihood
3.2.3 Conjugacy for a Beta prior on the probability of success, with a Binomial likelihood; see Gelman et al. (2004)
3.2.4 Conjugate prior for Normal linear regression; see Gelman et al. (2004)
3.2.5 Conditionally conjugate priors for random effects variances
3.2.6 Impropreity and Hierarchical Priors
3.2.7 Zellner's g -prior for regression models
3.2.8 Objective priors
3.3 Methodology II: Modelling Informative Priors
3.3.1 Informative modelling approaches
3.3.2 Elicitation of distributions
3.4 Case studies
3.4.1 Normal likelihood: Time to submit research dissertations
3.4.2 Binomial likelihood: Surveillance for exotic plant pests
3.4.3 Mixture model likelihood: Bioregionalisation
3.4.4 Logistic regression likelihood: Mapping species distribution via habitat models
3.5 Discussion
3.5.1 Limitations
3.5.2 Finding out about the problem
3.5.3 Prior formulation
3.5.4 Communication
3.5.5 Conclusion
3.6 Acknowledgements
References
4 Bayesian analysis of the Normal linear regression modelChristopher M. Strickland and Clair. L. Alston
4.1 Introduction
4.2 Case Studies	p. 1
4.2.1 Case Study 1: Boston Housing Data Set
4.2.2 Case Study 2: Production of Cars and Station wagons
4.3 Matrix notation and the likelihood
4.4 Posterior Inference
4.4.1 Natural Conjugate Prior
4.4.2 Alternative Prior Specifications
4.4.3 Generalisations of the normal linear model
4.4.4 Variable Selection
4.5 Analysis
4.5.1 Case Study : Boston housing data set
4.5.2 Case Study 2: Car production data set
References
5 Adapting ICU mortality models for local data: A Bayesian approachPetra L. Graham and Kerrie L. Mengersen and David A. Cook
5.1 Introduction
5.2 Case study: Updating a known risk-adjustment model for local use
5.3 Models and Methods
5.4 Data analysis and Results
5.4.1 Updating using the training data
5.4.2 Updating the model yearly
5.5 Discussion
References
6 A Bayesian Regression Model with Variable Selection for Genome-Wide Association StudiesCarla Chen and Kerrie L. Mengersen and Katja Ickstadt and Jonathan M. Keith
6.1 Introduction
6.2 Case study: Case-Control of Type I diabetes
6.3 Case study: GENICA
6.4 Models and Methods
6.4.1 Main effect models
6.4.2 Main effects and interactions
6.5 Data Analysis and Results
6.5.1 WTCCC-Type I diabetes
6.5.2 Genica
6.6 Discussion
References
6 A SNP IDs
7 Bayesian Meta-AnalysisJegar O. Pitchforth and Kerrie L. Mengersen
7.1 Introduction
7.2 Case Study 1: association between red meat consumption and breast cancer
7.2.1 Background
7.2.2 Meta-analysis models
7.2.3 Computation
7.2.4 Results
7.2.5 Discussion
7.3 Case study 2: Trends in fish growth rate and size
7.3.1 Background
7.3.2 Meta-analysis models
7.3.3 Computation
7.3.4 Results
7.3.5 Discussion
References
8 Bayesian mixed effects modelsClair L. Alston and Christopher M Strickland and Kerrie L. Mengersen and Graham E. Gardner
8.1 Introduction
8.2 Case studies
8.2.1 Case study 1: Hot carcase weight of sheep carcases
8.2.2 Case study 2: Growth of primary school girls
8.3 Models and Methods
8.3.1 Model for Case Study	p. 1
8.3.2 Model for Case Study	p. 2
8.3.3 MCMC estimation
8.4 Data Analysis and Results
8.5 Discussion
References
9 Ordering of Hierarchies in Hierarchical Models: Bone Mineral Density EstimationCathal D. Walsh and Kerrie L. Mengersen
9.1 Introduction
9.2 Case Study
9.2.1 Measurement of Bone Mineral Density
9.3 Models
9.3.1 Hierarchical Model
9.3.2 Model H1
9.3.3 Model H2
9.4 Data Analysis and Results
9.4.1 Model H1
9.4.2 Model H2
9.4.3 Implication of Ordering
9.4.4 Simulation Study
9.4.5 Study Design
9.4.6 Simulation Study Results
9.5 Discussion
References
9 A Likelihoods
10 BayesianWeibull Survival Model For Gene Expression DataSri Astuti Thamrin 1,2 and James M. McGree 1 and Kerrie L. Mengersen
10.1 Introduction
10.2 Survival Analyses
10.3 Bayesian Inference for The Weibull Survival Model
10.3.1 Weibull Model without Covariates
10.3.2 Weibull Model with Covariates
10.3.3 Model Evaluation and Comparison
10.4 Case Study
10.4.1 Weibull Model without Covariates
10.4.2 Weibull Survival Model with Covariates
10.4.3 Model Evaluation and Comparison
10.5 Discussion
References
11 Bayesian Change Point Detection in Monitoring Clinical OutcomesHassan Assareh and Ian Smith and Kerrie L. Mengersen
11.1 Introduction
11.2 Case Study: Monitoring Intensive Care Units Outcomes
11.3 Risk-Adjusted Control Charts
11.4 Change Point Model
11.5 Evaluation
11.6 Performance Analysis
11.7 Comparison of Bayesian Estimator with Other Methods
11.8 Conclusion
References
12 Bayesian SplinesSam Clifford and Sama Low Choy
12.1 Introduction
12.2 Models and methods
12.2.1 Splines and linear models
12.2.2 Link functions
12.2.3 Bayesian splines
12.2.4 Markov chain Monte Carlo
12.2.5 Model choice
12.2.6 Posterior diagnostics
12.3 Case Studies
12.3.1 Data
12.3.2 Analysis
12.4 Conclusion
12.4.1 Discussion
12.4.2 Extensions
12.4.3 Summary
References
13 Disease Mapping using Bayesian hierarchical modelsArul Earnest and Susanna M. Cramb and Nicole M. White
13.1 Introduction
13.2 Case Studies
13.2.1 Case study one: Spatio-temporal model examining the incidence of birth defects
13.2.2 Case study two: Relative survival model examining survival from breast cancer
13.3 Models and methods
13.3.1 Case study	p. 1
13.3.2 Case study	p. 2
13.4 Data Analysis and Results
13.4.1 Case study	p. 1
13.4.2 Case study	p. 2
13.5 Discussion
References
14 Moisture, crops and salination: an analysis of a three dimensional agricultural dataseMargaret Donald and Clair Alston and Rick Young and Kerrie Mengersen
14.1 Introduction
14.2 Case study
14.2.1 Data
14.2.2 Aim of the analysis
14.3 Review
14.3.1 General methodology
14.3.2 Computations
14.4 Case study modelling
14.4.1 Modelling framework
14.5 Model implementation: coding considerations
14.5.1 Neighbourhood matrices & CAR models
14.5.2 Design matrices vs indexing
14.6 Case study results
14.7 Conclusions
References
15 A Bayesian Approach to Multivariate State Space Modelling: A Study of a Fama-French Asset Pricing Model with Time Varying RegressorsChris M. Strickland and Philip Gharghori
15.1 Introduction
15.2 Case Study: Asst Pricing in Financial Markets
15.2.1 Data
15.3 Time Varying Fama-French Model
15.3.1 Specific models under consideration
15.4 Bayesian Estimation
15.4.1 Gibbs Sampler
15.4.2 Sampling _"
15.4.3 Sampling _ 1:n
15.4.4 Sampling __
15.4.5 Likelihood calculation
15.5 Analysis
15.5.1 Prior elicitation
15.5.2 Estimation output
15.6 Conclusion
References
16 Bayesian mixture models: When the thing you need to know is the thing you cannot measureClair L. Alston and Kerrie L. Mengersen and Graham E. Gardner
16.1 Introduction
16.2 Case study: CT scan images of sheep
16.3 Models and methods
16.3.1 Bayesian mixture models
16.3.2 Parameter estimation using the Gibbs Sampler
16.3.3 Extending the model to incorporate spatial information
16.4 Data Analysis and Results
16.4.1 Normal Bayesian mixture model
16.4.2 Spatial mixture model
16.4.3 Carcase volume calculation
16.5 Discussion
References
17 Latent Class Models in MedicineMargaret Rolfe and Nicole White and Carla Chen
17.1 Introduction
17.2 Case Studies
17.2.1 Case Study 1: Parkinson's Disease
17.2.2 Case Study 2: Cognition in Breast Cancer
17.3 Models and Methods
17.3.1 Finite mixture models
17.3.2 Trajectory Mixture Models
17.3.3 Goodness of fit
17.3.4 Label switching
17.3.5 Model computation
17.4 Data analysis and results
17.4.1 Case Study 1: Phenotype identification in Parkinson's disease

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Author Notes

Table of Contents