Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians

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