紹介
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.
目次
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 Integration Posterior Computations in R Fundamental Ideas II Statistical Testing Exchangeability Likelihood Functions Sufficient Statistics Analysis Using Predictive Distributions Flat Priors Jeffreys' Priors Bayes Factors Other Model Selection Criteria Normal Approximations to Posteriors Bayesian Consistency and Inconsistency Hierarchical Models Some Final Comments on Likelihoods Identifiability and Noninformative Data Comparing Populations Inference for Proportions Inference for Normal Populations Inference for Rates Sample Size Determination Illustrations: Foundry Data Medfly Data Radiological Contrast Data Reyes Syndrome Data Corrosion Data Diasorin Data Ache Hunting Data Breast Cancer Data Simulations Generating Random Samples Traditional Monte Carlo Methods Basics of Markov Chain Theory Markov Chain Monte Carlo Basic Concepts of Regression Introduction Data Notation and Format Predictive Models: An Overview Modeling with Linear Structures Illustration: FEV Data Binomial Regression The Sampling Model Binomial Regression Analysis Model Checking Prior Distributions Mixed Models Illustrations: Space Shuttle Data Trauma Data Onychomycosis Fungis Data Cow Abortion Data Linear Regression The Sampling Model Reference Priors Conjugate Priors Independence Priors ANOVA Model Diagnostics Model Selection Nonlinear Regression Illustrations: FEV Data Bank Salary Data Diasorin Data Coleman Report Data Dugong Growth Data Correlated Data Introduction Mixed Models Multivariate Normal Models Multivariate Normal Regression Posterior Sampling and Missing Data Illustrations: Interleukin Data Sleeping Dog Data Meta-Analysis Data Dental Data Count Data Poisson Regression Over-Dispersion and Mixtures of Poissons Longitudinal Data Illustrations: Ache Hunting Data Textile Faults Data Coronary Heart Disease Data Foot and Mouth Disease Data Time to Event Data Introduction One-Sample Models Two-Sample Data Plotting Survival and Hazard Functions Illustrations: Leukemia Cancer Data Breast Cancer Data Time to Event Regression Accelerated Failure Time Models Proportional Hazards Modeling Survival with Random Effects Illustrations: Leukemia Cancer Data Larynx Cancer Data Cow Abortion Data Kidney Transplant Data Lung Cancer Data Ache Hunting Data Binary Diagnostic Tests Basic Ideas One Test, One Population Two Tests, Two Populations Prevalence Distributions Illustrations: Coronary Artery Disease Paratuberculosis Data Nucleospora Salmonis Data Ovine Progressive Pnemonia Data Nonparametric Models Flexible Density Shapes Flexible Regression Functions Proportional Hazards Modeling Illustrations: Galaxy Data ELISA Data for Johnes Disease Fungus Data Test Engine Data Lung Cancer Data Appendix A: Matrices and Vectors Appendix B: Probability Appendix C: Getting Started in R References
