Christensen R. et al. Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians

CRC Press, 2011. — 518 p. — ISBN: 1439803544, 9781439803547.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 SimulationWinBUGS 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
Simulations
Generating Random Samples
Traditional Monte Carlo Methods
Basics of Markov Chain Theory
Markov Chain Monte Carlo
Basic Concepts of RegressionData 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
Linear Regression
The Sampling Model
Reference Priors
Conjugate Priors
Independence Priors
ANOVA
Model Diagnostics
Model Selection
Nonlinear Regression
Illustrations: FEV Data
Correlated DataMixed Models
Multivariate Normal Models
Multivariate Normal Regression
Posterior Sampling and Missing Data
Illustrations: Interleukin Data
Count Data
Poisson Regression
Over-Dispersion and Mixtures of Poissons
Longitudinal Data
Illustrations: Ache Hunting Data
Time to Event DataOne-Sample Models
Two-Sample Data
Plotting Survival and Hazard Functions
Illustrations: Leukemia Cancer Data
Time to Event Regression
Accelerated Failure Time Models
Proportional Hazards Modeling
Survival with Random Effects
Illustrations: Leukemia Cancer Data
Binary Diagnostic Tests
Basic Ideas
One Test, One Population
Two Tests, Two Populations
Prevalence Distributions
Illustrations: Coronary Artery Disease
Nonparametric Models
Flexible Density Shapes
Flexible Regression Functions
Proportional Hazards Modeling
Illustrations: Galaxy DataAppendix A: Matrices and Vectors
Appendix B: Probability
Appendix C: Getting Started in R