{"product_id":"case-studies-in-bayesian-statistical-modelling-and-analysis-isbn-9781119941828","title":"Case Studies in Bayesian Statistical Modelling and Analysis","description":"\u003cp\u003e\u003cb\u003eProvides an accessible foundation to Bayesian analysis using real world models\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eCase Studies in Bayesian Statistical Modelling and Analysis\u003c\/i\u003e:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eIllustrates how to do Bayesian analysis in a clear and concise manner using real-world problems.\u003c\/li\u003e \u003cli\u003eEach chapter focuses on a real-world problem and describes the way in which the problem may be analysed using Bayesian methods.\u003c\/li\u003e \u003cli\u003eFeatures 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.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eCase Studies in Bayesian Statistical Modelling and Analysis\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003eList of contributors xix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eClair L. Alston, Margaret Donald, Kerrie L. Mengersen and Anthony N. Pettitt\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Overview 1\u003c\/p\u003e \u003cp\u003e1.3 Further reading 8\u003c\/p\u003e \u003cp\u003e1.3.1 Bayesian theory and methodology 8\u003c\/p\u003e \u003cp\u003e1.3.2 Bayesian methodology 10\u003c\/p\u003e \u003cp\u003e1.3.3 Bayesian computation 10\u003c\/p\u003e \u003cp\u003e1.3.4 Bayesian software 11\u003c\/p\u003e \u003cp\u003e1.3.5 Applications 13\u003c\/p\u003e \u003cp\u003eReferences 13\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Introduction to MCMC 17\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eAnthony N. Pettitt and Candice M. Hincksman\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 17\u003c\/p\u003e \u003cp\u003e2.2 Gibbs sampling 18\u003c\/p\u003e \u003cp\u003e2.2.1 Example: Bivariate normal 18\u003c\/p\u003e \u003cp\u003e2.2.2 Example: Change-point model 19\u003c\/p\u003e \u003cp\u003e2.3 Metropolis–Hastings algorithms 19\u003c\/p\u003e \u003cp\u003e2.3.1 Example: Component-wise MH or MH within Gibbs 20\u003c\/p\u003e \u003cp\u003e2.3.2 Extensions to basic MCMC 21\u003c\/p\u003e \u003cp\u003e2.3.3 Adaptive MCMC 22\u003c\/p\u003e \u003cp\u003e2.3.4 Doubly intractable problems 22\u003c\/p\u003e \u003cp\u003e2.4 Approximate Bayesian computation 24\u003c\/p\u003e \u003cp\u003e2.5 Reversible jump MCMC 25\u003c\/p\u003e \u003cp\u003e2.6 MCMC for some further applications 26\u003c\/p\u003e \u003cp\u003eReferences 27\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Priors: Silent or active partners of Bayesian inference? 30\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eSamantha Low Choy\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Priors in the very beginning 30\u003c\/p\u003e \u003cp\u003e3.1.1 Priors as a basis for learning 32\u003c\/p\u003e \u003cp\u003e3.1.2 Priors and philosophy 32\u003c\/p\u003e \u003cp\u003e3.1.3 Prior chronology 33\u003c\/p\u003e \u003cp\u003e3.1.4 Pooling prior information 34\u003c\/p\u003e \u003cp\u003e3.2 Methodology I: Priors defined by mathematical criteria 35\u003c\/p\u003e \u003cp\u003e3.2.1 Conjugate priors 35\u003c\/p\u003e \u003cp\u003e3.2.2 Impropriety and hierarchical priors 37\u003c\/p\u003e \u003cp\u003e3.2.3 Zellner’s g-prior for regression models 37\u003c\/p\u003e \u003cp\u003e3.2.4 Objective priors 38\u003c\/p\u003e \u003cp\u003e3.3 Methodology II: Modelling informative priors 40\u003c\/p\u003e \u003cp\u003e3.3.1 Informative modelling approaches 40\u003c\/p\u003e \u003cp\u003e3.3.2 Elicitation of distributions 42\u003c\/p\u003e \u003cp\u003e3.4 Case studies 44\u003c\/p\u003e \u003cp\u003e3.4.1 Normal likelihood: Time to submit research dissertations 44\u003c\/p\u003e \u003cp\u003e3.4.2 Binomial likelihood: Surveillance for exotic plant pests 47\u003c\/p\u003e \u003cp\u003e3.4.3 Mixture model likelihood: Bioregionalization 50\u003c\/p\u003e \u003cp\u003e3.4.4 Logistic regression likelihood: Mapping species distribution via habitat models 53\u003c\/p\u003e \u003cp\u003e3.5 Discussion 57\u003c\/p\u003e \u003cp\u003e3.5.1 Limitations 57\u003c\/p\u003e \u003cp\u003e3.5.2 Finding out about the problem 58\u003c\/p\u003e \u003cp\u003e3.5.3 Prior formulation 59\u003c\/p\u003e \u003cp\u003e3.5.4 Communication 60\u003c\/p\u003e \u003cp\u003e3.5.5 Conclusion 61\u003c\/p\u003e \u003cp\u003eAcknowledgements 61\u003c\/p\u003e \u003cp\u003eReferences 61\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Bayesian analysis of the normal linear regression model 66\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eChristopher M. Strickland and Clair L. Alston\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 66\u003c\/p\u003e \u003cp\u003e4.2 Case studies 67\u003c\/p\u003e \u003cp\u003e4.2.1 Case study 1: Boston housing data set 67\u003c\/p\u003e \u003cp\u003e4.2.2 Case study 2: Production of cars and station wagons 67\u003c\/p\u003e \u003cp\u003e4.3 Matrix notation and the likelihood 67\u003c\/p\u003e \u003cp\u003e4.4 Posterior inference 68\u003c\/p\u003e \u003cp\u003e4.4.1 Natural conjugate prior 69\u003c\/p\u003e \u003cp\u003e4.4.2 Alternative prior specifications 73\u003c\/p\u003e \u003cp\u003e4.4.3 Generalizations of the normal linear model 74\u003c\/p\u003e \u003cp\u003e4.4.4 Variable selection 78\u003c\/p\u003e \u003cp\u003e4.5 Analysis 81\u003c\/p\u003e \u003cp\u003e4.5.1 Case study 1: Boston housing data set 81\u003c\/p\u003e \u003cp\u003e4.5.2 Case study 2: Car production data set 85\u003c\/p\u003e \u003cp\u003eReferences 88\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Adapting ICU mortality models for local data: A Bayesian approach 90\u003cbr\u003e\u003c\/b\u003e\u003ci\u003ePetra L. Graham, Kerrie L. Mengersen and David A. Cook\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 90\u003c\/p\u003e \u003cp\u003e5.2 Case study: Updating a known risk-adjustment model for local use 91\u003c\/p\u003e \u003cp\u003e5.3 Models and methods 92\u003c\/p\u003e \u003cp\u003e5.4 Data analysis and results 96\u003c\/p\u003e \u003cp\u003e5.4.1 Updating using the training data 96\u003c\/p\u003e \u003cp\u003e5.4.2 Updating the model yearly 98\u003c\/p\u003e \u003cp\u003e5.5 Discussion 100\u003c\/p\u003e \u003cp\u003eReferences 101\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 A Bayesian regression model with variable selection for genome-wide association studies 103\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eCarla Chen, Kerrie L. Mengersen, Katja Ickstadt and Jonathan M. Keith\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 103\u003c\/p\u003e \u003cp\u003e6.2 Case study: Case–control of Type 1 diabetes 104\u003c\/p\u003e \u003cp\u003e6.3 Case study: GENICA 105\u003c\/p\u003e \u003cp\u003e6.4 Models and methods 105\u003c\/p\u003e \u003cp\u003e6.4.1 Main effect models 105\u003c\/p\u003e \u003cp\u003e6.4.2 Main effects and interactions 108\u003c\/p\u003e \u003cp\u003e6.5 Data analysis and results 109\u003c\/p\u003e \u003cp\u003e6.5.1 WTCCC TID 109\u003c\/p\u003e \u003cp\u003e6.5.2 GENICA 110\u003c\/p\u003e \u003cp\u003e6.6 Discussion 112\u003c\/p\u003e \u003cp\u003eAcknowledgements 115\u003c\/p\u003e \u003cp\u003eReferences 115\u003c\/p\u003e \u003cp\u003e6.A  Appendix: SNP IDs 117\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Bayesian meta-analysis 118\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eJegar O. Pitchforth and Kerrie L. Mengersen\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 118\u003c\/p\u003e \u003cp\u003e7.2 Case study 1: Association between red meat consumption and breast cancer 119\u003c\/p\u003e \u003cp\u003e7.2.1 Background 119\u003c\/p\u003e \u003cp\u003e7.2.2 Meta-analysis models 121\u003c\/p\u003e \u003cp\u003e7.2.3 Computation 125\u003c\/p\u003e \u003cp\u003e7.2.4 Results 125\u003c\/p\u003e \u003cp\u003e7.2.5 Discussion 129\u003c\/p\u003e \u003cp\u003e7.3 Case study 2: Trends in fish growth rate and size 130\u003c\/p\u003e \u003cp\u003e7.3.1 Background 130\u003c\/p\u003e \u003cp\u003e7.3.2 Meta-analysis models 131\u003c\/p\u003e \u003cp\u003e7.3.3 Computation 134\u003c\/p\u003e \u003cp\u003e7.3.4 Results 134\u003c\/p\u003e \u003cp\u003e7.3.5 Discussion 135\u003c\/p\u003e \u003cp\u003eAcknowledgements 137\u003c\/p\u003e \u003cp\u003eReferences 138\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Bayesian mixed effects models 141\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eClair L. Alston, Christopher M. Strickland, Kerrie L. Mengersen and Graham E. Gardner\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 141\u003c\/p\u003e \u003cp\u003e8.2 Case studies 142\u003c\/p\u003e \u003cp\u003e8.2.1 Case study 1: Hot carcase weight of sheep carcases 142\u003c\/p\u003e \u003cp\u003e8.2.2 Case study 2: Growth of primary school girls 142\u003c\/p\u003e \u003cp\u003e8.3 Models and methods 146\u003c\/p\u003e \u003cp\u003e8.3.1 Model for Case study 1 147\u003c\/p\u003e \u003cp\u003e8.3.2 Model for Case study 2 148\u003c\/p\u003e \u003cp\u003e8.3.3 MCMC estimation 149\u003c\/p\u003e \u003cp\u003e8.4 Data analysis and results 150\u003c\/p\u003e \u003cp\u003e8.5 Discussion 158\u003c\/p\u003e \u003cp\u003eReferences 158\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Ordering of hierarchies in hierarchical models: Bone mineral density estimation 159\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eCathal D. Walsh and Kerrie L. Mengersen\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 159\u003c\/p\u003e \u003cp\u003e9.2 Case study 160\u003c\/p\u003e \u003cp\u003e9.2.1 Measurement of bone mineral density 160\u003c\/p\u003e \u003cp\u003e9.3 Models 161\u003c\/p\u003e \u003cp\u003e9.3.1 Hierarchical model 162\u003c\/p\u003e \u003cp\u003e9.3.2 Model H1 163\u003c\/p\u003e \u003cp\u003e9.3.3 Model H2 163\u003c\/p\u003e \u003cp\u003e9.4 Data analysis and results 164\u003c\/p\u003e \u003cp\u003e9.4.1 Model H1 164\u003c\/p\u003e \u003cp\u003e9.4.2 Model H2 165\u003c\/p\u003e \u003cp\u003e9.4.3 Implication of ordering 166\u003c\/p\u003e \u003cp\u003e9.4.4 Simulation study 166\u003c\/p\u003e \u003cp\u003e9.4.5 Study design 166\u003c\/p\u003e \u003cp\u003e9.4.6 Simulation study results 167\u003c\/p\u003e \u003cp\u003e9.5 Discussion 168\u003c\/p\u003e \u003cp\u003eReferences 168\u003c\/p\u003e \u003cp\u003e9.A  Appendix: Likelihoods 170\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Bayesian Weibull survival model for gene expression data 171\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eSri Astuti Thamrin, James M. McGree and Kerrie L. Mengersen\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 171\u003c\/p\u003e \u003cp\u003e10.2 Survival analysis 172\u003c\/p\u003e \u003cp\u003e10.3 Bayesian inference for the Weibull survival model 174\u003c\/p\u003e \u003cp\u003e10.3.1 Weibull model without covariates 174\u003c\/p\u003e \u003cp\u003e10.3.2 Weibull model with covariates 175\u003c\/p\u003e \u003cp\u003e10.3.3 Model evaluation and comparison 176\u003c\/p\u003e \u003cp\u003e10.4 Case study 178\u003c\/p\u003e \u003cp\u003e10.4.1 Weibull model without covariates 178\u003c\/p\u003e \u003cp\u003e10.4.2 Weibull survival model with covariates 180\u003c\/p\u003e \u003cp\u003e10.4.3 Model evaluation and comparison 182\u003c\/p\u003e \u003cp\u003e10.5 Discussion 182\u003c\/p\u003e \u003cp\u003eReferences 183\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Bayesian change point detection in monitoring clinical outcomes 186\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eHassan Assareh, Ian Smith and Kerrie L. Mengersen\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 186\u003c\/p\u003e \u003cp\u003e11.2 Case study: Monitoring intensive care unit outcomes 187\u003c\/p\u003e \u003cp\u003e11.3 Risk-adjusted control charts 187\u003c\/p\u003e \u003cp\u003e11.4 Change point model 188\u003c\/p\u003e \u003cp\u003e11.5 Evaluation 189\u003c\/p\u003e \u003cp\u003e11.6 Performance analysis 190\u003c\/p\u003e \u003cp\u003e11.7 Comparison of Bayesian estimator with other methods 194\u003c\/p\u003e \u003cp\u003e11.8 Conclusion 194\u003c\/p\u003e \u003cp\u003eReferences 195\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Bayesian splines 197\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eSamuel Clifford and Samantha Low Choy\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 197\u003c\/p\u003e \u003cp\u003e12.2 Models and methods 197\u003c\/p\u003e \u003cp\u003e12.2.1 Splines and linear models 197\u003c\/p\u003e \u003cp\u003e12.2.2 Link functions 198\u003c\/p\u003e \u003cp\u003e12.2.3 Bayesian splines 198\u003c\/p\u003e \u003cp\u003e12.2.4 Markov chain Monte Carlo 204\u003c\/p\u003e \u003cp\u003e12.2.5 Model choice 206\u003c\/p\u003e \u003cp\u003e12.2.6 Posterior diagnostics 207\u003c\/p\u003e \u003cp\u003e12.3 Case studies 207\u003c\/p\u003e \u003cp\u003e12.3.1 Data 207\u003c\/p\u003e \u003cp\u003e12.3.2 Analysis 208\u003c\/p\u003e \u003cp\u003e12.4 Conclusion 216\u003c\/p\u003e \u003cp\u003e12.4.1 Discussion 216\u003c\/p\u003e \u003cp\u003e12.4.2 Extensions 217\u003c\/p\u003e \u003cp\u003e12.4.3 Summary 218\u003c\/p\u003e \u003cp\u003eReferences 218\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Disease mapping using Bayesian hierarchical models 221\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eArul Earnest, Susanna M. Cramb and Nicole M. White\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 221\u003c\/p\u003e \u003cp\u003e13.2 Case studies 224\u003c\/p\u003e \u003cp\u003e13.2.1 Case study 1: Spatio-temporal model examining the incidence of birth defects 224\u003c\/p\u003e \u003cp\u003e13.2.2 Case study 2: Relative survival model examining survival from breast cancer 225\u003c\/p\u003e \u003cp\u003e13.3 Models and methods 225\u003c\/p\u003e \u003cp\u003e13.3.1 Case study 1 225\u003c\/p\u003e \u003cp\u003e13.3.2 Case study 2 229\u003c\/p\u003e \u003cp\u003e13.4 Data analysis and results 230\u003c\/p\u003e \u003cp\u003e13.4.1 Case study 1 230\u003c\/p\u003e \u003cp\u003e13.4.2 Case study 2 231\u003c\/p\u003e \u003cp\u003e13.5 Discussion 234\u003c\/p\u003e \u003cp\u003eReferences 237\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Moisture, crops and salination: An analysis of a three-dimensional agricultural data set 240\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eMargaret Donald, Clair L. Alston, Rick Young and Kerrie L. Mengersen\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 240\u003c\/p\u003e \u003cp\u003e14.2 Case study 241\u003c\/p\u003e \u003cp\u003e14.2.1 Data 242\u003c\/p\u003e \u003cp\u003e14.2.2 Aim of the analysis 242\u003c\/p\u003e \u003cp\u003e14.3 Review 243\u003c\/p\u003e \u003cp\u003e14.3.1 General methodology 243\u003c\/p\u003e \u003cp\u003e14.3.2 Computations 243\u003c\/p\u003e \u003cp\u003e14.4 Case study modelling 243\u003c\/p\u003e \u003cp\u003e14.4.1 Modelling framework 243\u003c\/p\u003e \u003cp\u003e14.5 Model implementation: Coding considerations 246\u003c\/p\u003e \u003cp\u003e14.5.1 Neighbourhood matrices and CAR models 246\u003c\/p\u003e \u003cp\u003e14.5.2 Design matrices vs indexing 246\u003c\/p\u003e \u003cp\u003e14.6 Case study results 247\u003c\/p\u003e \u003cp\u003e14.7 Conclusions 249\u003c\/p\u003e \u003cp\u003eReferences 250\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 A Bayesian approach to multivariate state space modelling: A study of a Fama–French asset-pricing model with time-varying regressors 252\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eChristopher M. Strickland and Philip Gharghori\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 252\u003c\/p\u003e \u003cp\u003e15.2 Case study: Asset pricing in financial markets 253\u003c\/p\u003e \u003cp\u003e15.2.1 Data 254\u003c\/p\u003e \u003cp\u003e15.3 Time-varying Fama–French model 254\u003c\/p\u003e \u003cp\u003e15.3.1 Specific models under consideration 255\u003c\/p\u003e \u003cp\u003e15.4 Bayesian estimation 256\u003c\/p\u003e \u003cp\u003e15.4.1 Gibbs sampler 256\u003c\/p\u003e \u003cp\u003e15.4.2 Sampling Σε 257\u003c\/p\u003e \u003cp\u003e15.4.3 Sampling β 1:n 257\u003c\/p\u003e \u003cp\u003e15.4.4 Sampling Σ\u003cb\u003e \u003c\/b\u003e α 259\u003c\/p\u003e \u003cp\u003e15.4.5 Likelihood calculation 260\u003c\/p\u003e \u003cp\u003e15.5 Analysis 261\u003c\/p\u003e \u003cp\u003e15.5.1 Prior elicitation 261\u003c\/p\u003e \u003cp\u003e15.5.2 Estimation output 261\u003c\/p\u003e \u003cp\u003e15.6 Conclusion 264\u003c\/p\u003e \u003cp\u003eReferences 265\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Bayesian mixture models: When the thing you need to know is the thing you cannot measure 267\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eClair L. Alston, Kerrie L. Mengersen and Graham E. Gardner\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 267\u003c\/p\u003e \u003cp\u003e16.2 Case study: CT scan images of sheep 268\u003c\/p\u003e \u003cp\u003e16.3 Models and methods 270\u003c\/p\u003e \u003cp\u003e16.3.1 Bayesian mixture models 270\u003c\/p\u003e \u003cp\u003e16.3.2 Parameter estimation using the Gibbs sampler 273\u003c\/p\u003e \u003cp\u003e16.3.3 Extending the model to incorporate spatial information 274\u003c\/p\u003e \u003cp\u003e16.4 Data analysis and results 276\u003c\/p\u003e \u003cp\u003e16.4.1 Normal Bayesian mixture model 276\u003c\/p\u003e \u003cp\u003e16.4.2 Spatial mixture model 278\u003c\/p\u003e \u003cp\u003e16.4.3 Carcase volume calculation 281\u003c\/p\u003e \u003cp\u003e16.5 Discussion 284\u003c\/p\u003e \u003cp\u003eReferences 284\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Latent class models in medicine 287\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eMargaret Rolfe, Nicole M. White and Carla Chen\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction 287\u003c\/p\u003e \u003cp\u003e17.2 Case studies 288\u003c\/p\u003e \u003cp\u003e17.2.1 Case study 1: Parkinson’s disease 288\u003c\/p\u003e \u003cp\u003e17.2.2 Case study 2: Cognition in breast cancer 288\u003c\/p\u003e \u003cp\u003e17.3 Models and methods 289\u003c\/p\u003e \u003cp\u003e17.3.1 Finite mixture models 290\u003c\/p\u003e \u003cp\u003e17.3.2 Trajectory mixture models 292\u003c\/p\u003e \u003cp\u003e17.3.3 Goodness of fit 296\u003c\/p\u003e \u003cp\u003e17.3.4 Label switching 297\u003c\/p\u003e \u003cp\u003e17.3.5 Model computation 298\u003c\/p\u003e \u003cp\u003e17.4 Data analysis and results 300\u003c\/p\u003e \u003cp\u003e17.4.1 Case study 1: Phenotype identification in PD 300\u003c\/p\u003e \u003cp\u003e17.4.2 Case study 2: Trajectory groups for verbal memory 302\u003c\/p\u003e \u003cp\u003e17.5 Discussion 306\u003c\/p\u003e \u003cp\u003eReferences 307\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Hidden Markov models for complex stochastic processes: A case study in electrophysiology 310\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eNicole M. White, Helen Johnson, Peter Silburn, Judith Rousseau and Kerrie L. Mengersen\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 310\u003c\/p\u003e \u003cp\u003e18.2 Case study: Spike identification and sorting of extracellular recordings 311\u003c\/p\u003e \u003cp\u003e18.3 Models and methods 312\u003c\/p\u003e \u003cp\u003e18.3.1 What is an HMM? 312\u003c\/p\u003e \u003cp\u003e18.3.2 Modelling a single AP: Application of a simple HMM 313\u003c\/p\u003e \u003cp\u003e18.3.3 Multiple neurons: An application of a factorial HMM 315\u003c\/p\u003e \u003cp\u003e18.3.4 Model estimation and inference 317\u003c\/p\u003e \u003cp\u003e18.4 Data analysis and results 320\u003c\/p\u003e \u003cp\u003e18.4.1 Simulation study 320\u003c\/p\u003e \u003cp\u003e18.4.2 Case study: Extracellular recordings collected during deep brain stimulation 323\u003c\/p\u003e \u003cp\u003e18.5 Discussion 326\u003c\/p\u003e \u003cp\u003eReferences 327\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Bayesian classification and regression trees 330\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eRebecca A. O’Leary, Samantha Low Choy, Wenbiao Hu and Kerrie L. Mengersen\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.1 Introduction 330\u003c\/p\u003e \u003cp\u003e19.2 Case studies 332\u003c\/p\u003e \u003cp\u003e19.2.1 Case study 1: Kyphosis 332\u003c\/p\u003e \u003cp\u003e19.2.2 Case study 2: Cryptosporidium 332\u003c\/p\u003e \u003cp\u003e19.3 Models and methods 334\u003c\/p\u003e \u003cp\u003e19.3.1 CARTs 334\u003c\/p\u003e \u003cp\u003e19.3.2 Bayesian CARTs 335\u003c\/p\u003e \u003cp\u003e19.4 Computation 337\u003c\/p\u003e \u003cp\u003e19.4.1 Building the BCART model – stochastic search 337\u003c\/p\u003e \u003cp\u003e19.4.2 Model diagnostics and identifying good trees 339\u003c\/p\u003e \u003cp\u003e19.5 Case studies – results 341\u003c\/p\u003e \u003cp\u003e19.5.1 Case study 1: Kyphosis 341\u003c\/p\u003e \u003cp\u003e19.5.2 Case study 2: Cryptosporidium 343\u003c\/p\u003e \u003cp\u003e19.6 Discussion 345\u003c\/p\u003e \u003cp\u003eReferences 346\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Tangled webs: Using Bayesian networks in the fight against infection 348\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eMary Waterhouse and Sandra Johnson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e20.1 Introduction to Bayesian network modelling 348\u003c\/p\u003e \u003cp\u003e20.1.1 Building a BN 349\u003c\/p\u003e \u003cp\u003e20.2 Introduction to case study 351\u003c\/p\u003e \u003cp\u003e20.3 Model 352\u003c\/p\u003e \u003cp\u003e20.4 Methods 354\u003c\/p\u003e \u003cp\u003e20.5 Results 355\u003c\/p\u003e \u003cp\u003e20.6 Discussion 357\u003c\/p\u003e \u003cp\u003eReferences 359\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Implementing adaptive dose finding studies using sequential Monte Carlo 361\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eJames M. McGree, Christopher C. Drovandi and Anthony N. Pettitt\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e21.1 Introduction 361\u003c\/p\u003e \u003cp\u003e21.2 Model and priors 363\u003c\/p\u003e \u003cp\u003e21.3 SMC for dose finding studies 364\u003c\/p\u003e \u003cp\u003e21.3.1 Importance sampling 364\u003c\/p\u003e \u003cp\u003e21.3.2 SMC 365\u003c\/p\u003e \u003cp\u003e21.3.3 Dose selection procedure 367\u003c\/p\u003e \u003cp\u003e21.4 Example 369\u003c\/p\u003e \u003cp\u003e21.5 Discussion 371\u003c\/p\u003e \u003cp\u003eReferences 372\u003c\/p\u003e \u003cp\u003e21.A Appendix: Extra example 373\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 Likelihood-free inference for transmission rates of nosocomial pathogens 374\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eChristopher C. Drovandi and Anthony N. Pettitt\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e22.1 Introduction 374\u003c\/p\u003e \u003cp\u003e22.2 Case study: Estimating transmission rates of nosocomial pathogens 375\u003c\/p\u003e \u003cp\u003e22.2.1 Background 375\u003c\/p\u003e \u003cp\u003e22.2.2 Data 376\u003c\/p\u003e \u003cp\u003e22.2.3 Objective 376\u003c\/p\u003e \u003cp\u003e22.3 Models and methods 376\u003c\/p\u003e \u003cp\u003e22.3.1 Models 376\u003c\/p\u003e \u003cp\u003e22.3.2 Computing the likelihood 379\u003c\/p\u003e \u003cp\u003e22.3.3 Model simulation 380\u003c\/p\u003e \u003cp\u003e22.3.4 ABC 381\u003c\/p\u003e \u003cp\u003e22.3.5 ABC algorithms 382\u003c\/p\u003e \u003cp\u003e22.4 Data analysis and results 384\u003c\/p\u003e \u003cp\u003e22.5 Discussion 385\u003c\/p\u003e \u003cp\u003eReferences 386\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 Variational Bayesian inference for mixture models 388\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eClare A. McGrory\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e23.1 Introduction 388\u003c\/p\u003e \u003cp\u003e23.2 Case study: Computed tomography (CT) scanning of a loin portion of a pork carcase 390\u003c\/p\u003e \u003cp\u003e23.3 Models and methods 392\u003c\/p\u003e \u003cp\u003e23.4 Data analysis and results 397\u003c\/p\u003e \u003cp\u003e23.5 Discussion 399\u003c\/p\u003e \u003cp\u003eReferences 399\u003c\/p\u003e \u003cp\u003e23.A Appendix: Form of the variational posterior for a mixture of multivariate normal densities 401\u003c\/p\u003e \u003cp\u003e\u003cb\u003e24 Issues in designing hybrid algorithms 403\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eJeong E. Lee, Kerrie L. Mengersen and Christian P. Robert\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e24.1 Introduction 403\u003c\/p\u003e \u003cp\u003e24.2 Algorithms and hybrid approaches 406\u003c\/p\u003e \u003cp\u003e24.2.1 Particle system in the MCMC context 407\u003c\/p\u003e \u003cp\u003e24.2.2 MALA 407\u003c\/p\u003e \u003cp\u003e24.2.3 DRA 408\u003c\/p\u003e \u003cp\u003e24.2.4 PS 409\u003c\/p\u003e \u003cp\u003e24.2.5 Population Monte Carlo (PMC) algorithm 410\u003c\/p\u003e \u003cp\u003e24.3 Illustration of hybrid algorithms 412\u003c\/p\u003e \u003cp\u003e24.3.1 Simulated data set 412\u003c\/p\u003e \u003cp\u003e24.3.2 Application: Aerosol particle size 415\u003c\/p\u003e \u003cp\u003e24.4 Discussion 417\u003c\/p\u003e \u003cp\u003eReferences 418\u003c\/p\u003e \u003cp\u003e\u003cb\u003e25 A Python package for Bayesian estimation using Markov chain Monte Carlo 421\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eChristopher M. Strickland, Robert J. Denham, Clair L. Alston and Kerrie L. Mengersen\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e25.1 Introduction 421\u003c\/p\u003e \u003cp\u003e25.2 Bayesian analysis 423\u003c\/p\u003e \u003cp\u003e25.2.1 MCMC methods and implementation 424\u003c\/p\u003e \u003cp\u003e25.2.2 Normal linear Bayesian regression model 433\u003c\/p\u003e \u003cp\u003e25.3 Empirical illustrations 437\u003c\/p\u003e \u003cp\u003e25.3.1 Example 1: Linear regression model – variable selection and estimation 438\u003c\/p\u003e \u003cp\u003e25.3.2 Example 2: Loglinear model 441\u003c\/p\u003e \u003cp\u003e25.3.3 Example 3: First-order autoregressive regression 446\u003c\/p\u003e \u003cp\u003e25.4 Using PyMCMC efficiently 451\u003c\/p\u003e \u003cp\u003e25.4.1 Compiling code in Windows 455\u003c\/p\u003e \u003cp\u003e25.5 PyMCMC interacting with R 457\u003c\/p\u003e \u003cp\u003e25.6 Conclusions 458\u003c\/p\u003e \u003cp\u003e25.7 Obtaining PyMCMC 459\u003c\/p\u003e \u003cp\u003eReferences 459\u003c\/p\u003e \u003cp\u003eIndex 461 \u003c\/p\u003e \u003cp\u003e“As such, this book can serve as a handy reference for proficient statisticians and programmers.”  (\u003ci\u003eThe Quarterly Review of Biology\u003c\/i\u003e, 1 October 2015)\u003c\/p\u003e  \u003cp\u003e\u003cstrong\u003eClair Alston\u003c\/strong\u003e, Queensland University of Technology and Science, Australia. \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eKerrie L. Mengersen\u003c\/strong\u003e, Queensland University of Technology and Science, Australia. \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eTony Pettitt\u003c\/strong\u003e, Queensland University of Technology and Science, Australia.   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eProvides an accessible foundation to Bayesian analysis using real world models\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis 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\u003c\/p\u003e \u003cp\u003e\u003ci\u003eCase Studies in Bayesian Statistical Modelling and Analysis\u003c\/i\u003e:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eIllustrates how to do Bayesian analysis in a clear and concise manner using real-world problems.\u003c\/li\u003e \u003cli\u003eEach chapter focuses on a real-world problem and describes the way in which the problem may be analysed using Bayesian methods.\u003c\/li\u003e \u003cli\u003eFeatures 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.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eCase Studies in Bayesian Statistical Modelling and Analysis\u003c\/i\u003e 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988890075365,"sku":"NP9781119941828","price":117.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119941828.jpg?v=1761781936","url":"https:\/\/k12savings.com\/products\/case-studies-in-bayesian-statistical-modelling-and-analysis-isbn-9781119941828","provider":"K12savings","version":"1.0","type":"link"}