Bayesian Ideas and Data Analysis An Introduction for Scientists and Statisticians

Emphasizing the use of WinBUGS and R to analyze real data, Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians presents statistical tools to address scientific questions. It highlights foundational issues in statistics, the importance of making accurate predictions, and the need for scientists and statisticians to collaborate in analyzing data. The WinBUGS code provided offers a convenient platform to model and analyze a wide range of data. The first five chapters of the book contain core material that spans basic Bayesian ideas, calculations, and inference, including modeling one and two sample data from traditional sampling models. The text then covers Monte Carlo methods, such as Markov chain Monte Carlo (MCMC) simulation. After discussing linear structures in regression, it presents binomial regression, normal regression, analysis of variance, and Poisson regression, before extending these methods to handle correlated data. The authors also examine survival analysis and binary diagnostic testing. A complementary chapter on diagnostic testing for continuous outcomes is available on the book’s website. The last chapter on nonparametric inference explores density estimation and flexible regression modeling of mean functions. The appropriate statistical analysis of data involves a collaborative effort between scientists and statisticians. Exemplifying this approach, Bayesian Ideas and Data Analysis focuses on the necessary tools and concepts for modeling and analyzing scientific data. Data sets and codes are provided on a supplemental website.

Prologue Probability of a Defective: Binomial Data Brass Alloy Zinc Content: Normal Data Armadillo Hunting: Poisson Data Abortion in Dairy Cattle: Survival Data Ache Hunting with Age Trends Lung Cancer Treatment: Log-Normal Regression Survival with Random Effects: Ache Hunting Fundamental Ideas I Simple Probability Computations Science, Priors, and Prediction Statistical Models Posterior Analysis Commonly Used Distributions Integration versus Simulation Introduction WinBUGS I: Getting Started Method of Composition Monte Carlo IntegrationPosterior Computations in R Fundamental Ideas IIStatistical TestingExchangeability Likelihood Functions Sufficient Statistics Analysis Using Predictive Distributions Flat Priors Jeffreys’ Priors Bayes FactorsOther Model Selection CriteriaNormal Approximations to PosteriorsBayesian Consistency and Inconsistency Hierarchical Models Some Final Comments on LikelihoodsIdentifiability and Noninformative Data Comparing Populations Inference for ProportionsInference for Normal PopulationsInference for RatesSample Size DeterminationIllustrations: Foundry Data Medfly Data Radiological Contrast Data Reyes Syndrome DataCorrosion DataDiasorin DataAche Hunting DataBreast Cancer Data Simulations Generating Random Samples Traditional Monte Carlo MethodsBasics of Markov Chain TheoryMarkov Chain Monte Carlo Basic Concepts of RegressionIntroduction Data Notation and Format Predictive Models: An Overview Modeling with Linear StructuresIllustration: FEV Data Binomial RegressionThe Sampling Model Binomial Regression AnalysisModel CheckingPrior DistributionsMixed ModelsIllustrations: Space Shuttle Data Trauma DataOnychomycosis Fungis DataCow Abortion Data Linear RegressionThe Sampling Model Reference PriorsConjugate Priors Independence Priors ANOVAModel Diagnostics Model SelectionNonlinear RegressionIllustrations: FEV Data Bank Salary DataDiasorin DataColeman Report DataDugong Growth Data Correlated Data Introduction Mixed Models Multivariate Normal Models Multivariate Normal Regression Posterior Sampling and Missing DataIllustrations: Interleukin Data Sleeping Dog DataMeta-Analysis DataDental Data Count Data Poisson RegressionOver-Dispersion and Mixtures of PoissonsLongitudinal DataIllustrations: Ache Hunting Data Textile Faults DataCoronary Heart Disease DataFoot and Mouth Disease Data Time to Event DataIntroductionOne-Sample ModelsTwo-Sample DataPlotting Survival and Hazard FunctionsIllustrations: Leukemia Cancer Data Breast Cancer Data Time to Event Regression Accelerated Failure Time ModelsProportional Hazards ModelingSurvival with Random EffectsIllustrations: Leukemia Cancer Data Larynx Cancer DataCow Abortion DataKidney Transplant DataLung Cancer DataAche Hunting Data Binary Diagnostic Tests Basic Ideas One Test, One Population Two Tests, Two Populations Prevalence DistributionsIllustrations: Coronary Artery Disease Paratuberculosis DataNucleospora Salmonis DataOvine Progressive Pnemonia Data Nonparametric ModelsFlexible Density ShapesFlexible Regression Functions Proportional Hazards ModelingIllustrations: Galaxy Data ELISA Data for Johnes DiseaseFungus DataTest Engine DataLung Cancer Data Appendix A: Matrices and VectorsAppendix B: ProbabilityAppendix C: Getting Started in R References

Ronald Christensen is a Professor in the Department of Mathematics and Statistics at the University of New Mexico, Albuquerque. He is also a Fellow of the American Statistical Association (ASA) and the Institute of Mathematical Statistics as well as the former Chair of the ASA Section on Bayesian Statistical Science. Wesley Johnson is a Professor in the Department of Statistics at the University of California, Irvine. He is also a Fellow of the ASA and Chair-Elect of the ASA Section on Bayesian Statistical Science. Adam Branscum is an Associate Professor in the Department of Public Health at Oregon State University, Corvallis. Timothy E. Hanson is an Associate Professor in the Department of Statistics at the University of South Carolina, Columbia.