There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis obtainable to a wide audience. This book provides an accessible approach to Bayesian data analysis, as material is explained clearly with concrete examples.
This book begins with the basics, including essential concepts of probability and random sampling, and gradually progresses to advanced hierarchical modeling methods for realistic data. The text delivers comprehensive coverage of all scenarios addressed by non-Bayesian textbooks - t-tests, analysis of variance (ANOVA) and comparisons in ANOVA, multiple regression, and chi-square (contingency table analysis).
- This Book's Organization: Read me First!
- The Basics: Parameters, Probability, Bayes' Rule and R
- What is this stuff called probability?
- Bayes' Rule
Part II All the Fundamental Concepts and Techniques in a Simple Scenario
- Inferring a Binomial Proportion via Exact mathematical Analysis
- Inferring a Binomial Proportion via Grid Approximation
- Inferring a Binomial Proportion via Monte Carlo Methods
- Inferences Regarding Two Binomial Proportions
- Bernoulli Likelihood with Hierarchical Prior
- Hierarchical modeling and model comparison
- Null Hypothesis Significance Testing
- Bayesian Approaches to Testing a Point ("Null") Hypothesis
- Goals, Power, and Sample Size
Part III The Generalized Linear Model
- Overview of the Generalized Linear Model
- Metric Predicted Variable on a Single Group
- Metric Predicted Variable with One Metric Predictor
- Metric Predicted Variable with Multiple Metric Predictors
- Metric Predicted Variable with One Nominal Predictor
- Metric Predicted Variable with Multiple Nominal Predictors
- Dichotomous Predicted Variable
- Original Predicted Variable, Contingency Table Analysis
Part IV Tools in the Trunk
- Reparameterization, a.k.a. Change of Variables