Chapter 1: What's in This Book (Read This First!)

• 1.1 Real people can read this book
• 1.2 What's in this book
• 1.3 What's new in the second edition?
• 1.4 Gimme feedback (Be polite)
• 1.5 Thank you!

Part I: The Basics: Models, Probability, Bayes’ Rule, and R

Introduction

Chapter 2: Introduction: Credibility, Models, and Parameters

• 2.1 Bayesian inference is reallocation of credibility across possibilities
• 2.2 Possibilities are parameter values in descriptive models
• 2.3 The steps of bayesian data analysis
• 2.4 Exercises

Chapter 3: The R Programming Language

• 3.1 Get the software
• 3.2 A simple example of R in action
• 3.3 Basic commands and operators in R
• 3.4 Variable types
• 3.5 Loading and saving data
• 3.6 Some utility functions
• 3.7 Programming in R
• 3.8 Graphical plots: Opening and saving
• 3.9 Conclusion
• 3.10 Exercises

Chapter 4: What is This Stuff Called Probability?

• 4.1 The set of all possible events
• 4.2 Probability: Outside or inside the head
• 4.3 Probability distributions
• 4.4 Two-way distributions
• 4.5 Appendix: R code for figure 4.1
• 4.6 Exercises

Chapter 5: Bayes' Rule

• 5.1 Bayes' rule
• 5.2 Applied to parameters and data
• 5.3 Complete examples: Estimating bias in a coin
• 5.4 Why bayesian inference can be difficult
• 5.5 Appendix: R code for figures 5.1, 5.2, etc.
• 5.6 Exercises

Part II: All the Fundamentals Applied to Inferring a Binomial Probability

Introduction

Chapter 6: Inferring a Binomial Probability via Exact Mathematical Analysis

• 6.1 The likelihood function: Bernoulli distribution
• 6.2 A description of credibilities: The beta distribution
• 6.3 The posterior beta
• 6.4 Examples
• 6.5 Summary
• 6.6 Appendix: R code for figure 6.4
• 6.7 Exercises

Chapter 7: Markov Chain Monte Carlo

• 7.1 Approximating a distribution with a large sample
• 7.2 A simple case of the metropolis algorithm
• 7.3 The metropolis algorithm more generally
• 7.4 Toward gibbs sampling: Estimating two coin biases
• 7.5 Mcmc representativeness, accuracy, and efficiency
• 7.6 Summary
• 7.7 Exercises

Chapter 8: JAGS

• 8.1 Jags and its relation to R
• 8.2 A complete example
• 8.3 Simplified scripts for frequently used analyses
• 8.4 Example: difference of biases
• 8.5 Sampling from the prior distribution in jags
• 8.6 Probability distributions available in jags
• 8.7 Faster sampling with parallel processing in runjags
• 8.8 Tips for expanding jags models
• 8.9 Exercises

Chapter 9: Hierarchical Models

• 9.1 A single coin from a single mint
• 9.2 Multiple coins from a single mint
• 9.3 Shrinkage in hierarchical models
• 9.4 Speeding up jags
• 9.5 Extending the hierarchy: Subjects within categories
• 9.6 Exercises

Chapter 10: Model Comparison and Hierarchical Modeling

• 10.1 General formula and the bayes factor
• 10.2 Example: two factories of coins
• 10.3 Solution by MCMC
• 10.4 Prediction: Model averaging
• 10.5 Model complexity naturally accounted for
• 10.6 Extreme sensitivity to prior distribution
• 10.7 Exercises

Chapter 11: Null Hypothesis Significance Testing

• 11.1 Paved with good intentions
• 11.2 Prior knowledge
• 11.3 Confidence interval and highest density interval
• 11.4 Multiple comparisons
• 11.5 What a sampling distribution is good for
• 11.6 Exercises

Chapter 12: Bayesian Approaches to Testing a Point (“Null¿) Hypothesis

• 12.1 The estimation approach
• 12.2 The model-comparison approach
• 12.3 Relations of parameter estimation and model comparison
• 12.4. Estimation or model comparison?
• 12.5. Exercises

Chapter 13: Goals, Power, and Sample Size

• 13.1 The will to power
• 13.2 Computing power and sample size
• 13.3 Sequential testing and the goal of precision
• 13.4 Discussion
• 13.5 Exercises

Chapter 14: Stan

• 14.1 HMC sampling
• 14.2 Installing stan
• 14.3 A complete example
• 14.4 Specify models top-down in stan
• 14.5 Limitations and extras
• 14.6 Exercises

Part III: The Generalized Linear Model

Introduction

Chapter 15: Overview of the Generalized Linear Model

• 15.1 Types of variables
• 15.2 Linear combination of predictors
• 15.3 Linking from combined predictors to noisy predicted data
• 15.4 Formal expression of the GLM
• 15.5 Exercises

Chapter 16: Metric-Predicted Variable on One or Two Groups

• 16.1 Estimating the mean and standard deviation of a normal distribution
• 16.2 Outliers and robust estimation: The t distribution
• 16.3 Two groups
• 16.4 Other noise distributions and transforming data
• 16.5 Exercises

Chapter 17: Metric Predicted Variable with One Metric Predictor

• 17.1 Simple linear regression
• 17.2 Robust linear regression
• 17.3 Hierarchical regression on individuals within groups
• 17.4 Quadratic trend and weighted data
• 17.5 Procedure and perils for expanding a model
• 17.6 Exercises

Chapter 18: Metric Predicted Variable with Multiple Metric Predictors

• 18.1 Multiple linear regression
• 18.2 Multiplicative interaction of metric predictors
• 18.3 Shrinkage of regression coefficients
• 18.4 Variable selection
• 18.5 Exercises

Chapter 19: Metric Predicted Variable with One Nominal Predictor

• 19.1 Describing multiple groups of metric data
• 19.2 Traditional analysis of variance
• 19.3 Hierarchical bayesian approach
• 19.4 Including a metric predictor
• 19.5 Heterogeneous variances and robustness against outliers
• 19.6 Exercises

Chapter 20: Metric Predicted Variable with Multiple Nominal Predictors

• 20.1 Describing groups of metric data with multiple nominal predictors
• 20.2 Hierarchical bayesian approach
• 20.3 Rescaling can change interactions, homogeneity, and normality
• 20.4 Heterogeneous variances and robustness against outliers
• 20.5 Within-subject designs
• 20.6 Model comparison approach
• 20.7 Exercises

Chapter 21: Dichotomous Predicted Variable

• 21.1 Multiple metric predictors
• 21.2 Interpreting the regression coefficients
• 21.3 Robust logistic regression
• 21.4 Nominal predictors
• 21.5 Exercises

Chapter 22: Nominal Predicted Variable

• 22.1 Softmax regression
• 22.2 Conditional logistic regression
• 22.3 Implementation in jags
• 22.4 Generalizations and variations of the models
• 22.5 Exercises

Chapter 23: Ordinal Predicted Variable

• 23.1 Modeling ordinal data with an underlying metric variable
• 23.2 The case of a single group
• 23.3 The case of two groups
• 23.4 The case of metric predictors
• 23.5 Posterior prediction
• 23.6 Generalizations and extensions
• 23.7 Exercises

Chapter 24: Count Predicted Variable

• 24.1 Poisson exponential model
• 24.2 Example: hair eye go again
• 24.3 Example: interaction contrasts, shrinkage, and omnibus test
• 24.4 Log-linear models for contingency tables
• 24.5 Exercises

Chapter 25: Tools in the Trunk

• 25.1 Reporting a bayesian analysis
• 25.2 Functions for computing highest density intervals
• 25.3 Reparameterization
• 25.4 Censored data in JAGS
• 25.5 What next?