Case Studies in Bayesian Statistical Modelling and Analysis -- Contents -- Preface -- List of contributors -- 1 Introduction -- 1.1 Introduction -- 1.2 Overview -- 1.3 Further reading -- 1.3.1 Bayesian theory and methodology -- 1.3.2 Bayesian methodology -- 1.3.3 Bayesian computation -- 1.3.4 Bayesian software -- 1.3.5 Applications -- References -- 2 Introduction to MCMC -- 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 problems -- 2.4 Approximate Bayesian computation -- 2.5 Reversible jump MCMC -- 2.6 MCMC for some further applications -- References -- 3 Priors: Silent or active partners of Bayesian inference? -- 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 Impropriety and hierarchical priors -- 3.2.3 Zellner's g-prior for regression models -- 3.2.4 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: Bioregionalization -- 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 -- Acknowledgements -- References.

4 Bayesian analysis of the normal linear regression model -- 4.1 Introduction -- 4.2 Case studies -- 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 Generalizations of the normal linear model -- 4.4.4 Variable selection -- 4.5 Analysis -- 4.5.1 Case study 1: 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 approach -- 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 studies -- 6.1 Introduction -- 6.2 Case study: Case-control of Type 1 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 TID -- 6.5.2 GENICA -- 6.6 Discussion -- Acknowledgements -- References -- 6.A Appendix: SNP IDs -- 7 Bayesian meta-analysis -- 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 -- Acknowledgements -- References -- 8 Bayesian mixed effects models -- 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 1 -- 8.3.2 Model for Case study 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 estimation -- 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 Appendix: Likelihoods -- 10 Bayesian Weibull survival model for gene expression data -- 10.1 Introduction -- 10.2 Survival analysis -- 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 outcomes -- 11.1 Introduction -- 11.2 Case study: Monitoring intensive care unit 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 splines -- 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 models -- 13.1 Introduction -- 13.2 Case studies -- 13.2.1 Case study 1: Spatio-temporal model examining the incidence of birth defects -- 13.2.2 Case study 2: Relative survival model examining survival from breast cancer -- 13.3 Models and methods -- 13.3.1 Case study 1 -- 13.3.2 Case study 2 -- 13.4 Data analysis and results -- 13.4.1 Case study 1 -- 13.4.2 Case study 2 -- 13.5 Discussion -- References -- 14 Moisture, crops and salination: An analysis of a three-dimensional agricultural data set -- 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 and 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 regressors -- 15.1 Introduction -- 15.2 Case study: Asset 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 Σε -- 15.4.3 Sampling β1:n -- 15.4.4 Sampling Σα -- 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 measure -- 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 medicine -- 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 PD -- 17.4.2 Case study 2: Trajectory groups for verbal memory -- 17.5 Discussion -- References -- 18 Hidden Markov models for complex stochastic processes: A case study in electrophysiology -- 18.1 Introduction -- 18.2 Case study: Spike identification and sorting of extracellular recordings -- 18.3 Models and methods -- 18.3.1 What is an HMM? -- 18.3.2 Modelling a single AP: Application of a simple HMM -- 18.3.3 Multiple neurons: An application of a factorial HMM -- 18.3.4 Model estimation and inference -- 18.4 Data analysis and results -- 18.4.1 Simulation study -- 18.4.2 Case study: Extracellular recordings collected during deep brain stimulation -- 18.5 Discussion -- References -- 19 Bayesian classification and regression trees -- 19.1 Introduction -- 19.2 Case studies -- 19.2.1 Case study 1: Kyphosis -- 19.2.2 Case study 2: Cryptosporidium -- 19.3 Models and methods -- 19.3.1 CARTs -- 19.3.2 Bayesian CARTs -- 19.4 Computation -- 19.4.1 Building the BCART model - stochastic search -- 19.4.2 Model diagnostics and identifying good trees -- 19.5 Case studies - results -- 19.5.1 Case study 1: Kyphosis.

19.5.2 Case study 2: Cryptosporidium.