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Index
Cover Image
Table of Contents
Front Matter
Copyright
Dedication
Chapter 1. This Book's Organization
1.1. Real People can Read This Book
1.2. Prerequisites
1.3. The Organization of This Book
1.4. Gimme Feedback (Be Polite)
1.5. Acknowledgments
Chapter 2. Introduction
2.1. Models of Observations and Models of Beliefs
2.2. Three Goals for Inference from Data
2.3. The R Programming Language
2.4. Exercises
Chapter 3. What Is This Stuff Called Probability?
3.1. The Set of All Possible Events
3.2. Probability: Outside or Inside the Head
3.3. Probability Distributions
3.4. Two-Way Distributions
3.5. R Code
3.6. Exercises
Chapter 4. Bayes' Rule
4.1. Bayes' Rule
4.2. Applied to Models and Data
4.3. The Three Goals of Inference
4.4. R Code
4.5. Exercises
Chapter 5. Inferring a Binomial Proportion via Exact Mathematical Analysis
5.1. The Likelihood Function: Bernoulli Distribution
5.2. A Description of Beliefs: The Beta Distribution
5.3. Three Inferential Goals
5.4. Summary: How to do Bayesian Inference
5.5. R Code
5.6. Exercises
Chapter 6. Inferring a Binomial Proportion via Grid Approximation
6.1. Bayes' Rule for Discrete Values of θ
6.2. Discretizing a Continuous Prior Density
6.3. Estimation
6.4. Prediction of Subsequent Data
6.5. Model Comparison
6.6. Summary
6.7. R Code
6.8. Exercises
Chapter 7. Inferring a Binomial Proportion via the Metropolis Algorithm
7.1. A Simple Case of the Metropolis Algorithm
7.2. The Metropolis Algorithm More Generally
7.3. From the Sampled Posterior to the Three Goals
7.4. MCMC in BUGS
7.5. Conclusion
7.6. R Code
7.7. Exercises
Chapter 8. Inferring Two Binomial Proportions via Gibbs Sampling
8.1. Prior, Likelihood, and Posterior for Two Proportions
8.2. The Posterior via Exact Formal Analysis
8.3. The Posterior via Grid Approximation
8.4. The Posterior via Markov Chain Monte Carlo
8.5. Doing it with BUGS
8.6. How Different are the Underlying Biases?
8.7. Summary
8.8. R Code
8.9. Exercises
Chapter 9. Bernoulli Likelihood with Hierarchical Prior
9.1. A Single Coin from a Single Mint
9.2. Multiple Coins from a Single Mint
9.3. Multiple Coins from Multiple Mints
9.4. Summary
9.5. R Code
9.6. Exercises
Chapter 10. Hierarchical Modeling and Model Comparison
10.1. Model Comparison as Hierarchical Modeling
10.2. Model Comparison in BUGS
10.3. Model Comparison and Nested Models
10.4. Review of Hierarchical Framework for Model Comparison
10.5. Exercises
Chapter 11. Null Hypothesis Significance Testing
11.1. NHST for the Bias of a Coin
11.2. Prior Knowledge about the Coin
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 (Single Prior) Approach
12.2. The Model-Comparison (Two-Prior) Approach
12.3. Estimation or Model Comparison?
12.4. R Code
12.5. Exercises
Chapter 13. Goals, Power, and Sample Size
13.1. The Will to Power
13.2. Sample Size for a Single Coin
13.3. Sample Size for Multiple Mints
13.4. Power: Prospective, Retrospective, and Replication
13.5. The Importance of Planning
13.6. R Code
13.7. Exercises
Chapter 14. Overview of the Generalized Linear Model
14.1. The Generalized Linear Model (GLM)
14.2. Cases of the GLM
14.3. Exercises
Chapter 15. Metric Predicted Variable on a Single Group
15.1. Estimating the Mean and Precision of a Normal Likelihood
15.2. Repeated Measures and Individual Differences
15.3. Summary
15.4. R Code
15.5. Exercises
Chapter 16. Metric Predicted Variable with One Metric Predictor
16.1. Simple Linear Regression
16.2. Outliers and Robust Regression
16.3. Simple Linear Regression with Repeated Measures
16.4. Summary
16.5. R Code
16.6. Exercises
Chapter 17. Metric Predicted Variable with Multiple Metric Predictors
17.1. Multiple Linear Regression
17.2. Hyperpriors and Shrinkage of Regression Coefficients
17.3. Multiplicative Interaction of Metric Predictors
17.4. Which Predictors should be Included?
17.5. R Code
17.6. Exercises
Chapter 18. Metric Predicted Variable with One Nominal Predictor
18.1. Bayesian Oneway ANOVA
18.2. Multiple Comparisons
18.3. Two-Group Bayesian ANOVA and the NHST t Test
18.4. R Code
18.5. Exercises
Chapter 19. Metric Predicted Variable with Multiple Nominal Predictors
19.1. Bayesian Multifactor ANOVA
19.2. Repeated Measures, a.k.a. Within-Subject Designs
19.3. R Code
19.4. Exercises
Chapter 20. Dichotomous Predicted Variable
20.1. Logistic Regression
20.2. Interaction of Predictors in Logistic Regression
20.3. Logistic ANOVA
20.4. Summary
20.5. R Code
20.6. Exercises
Chapter 21. Ordinal Predicted Variable
21.1. Ordinal Probit Regression
21.2. Some Examples
21.3. Interaction
21.4. Relation to Linear and Logistic Regression
21.5. R Code
21.6. Exercises
Chapter 22. Contingency Table Analysis
22.1. Poisson Exponential ANOVA
22.2. Examples
22.3. Log Linear Models for Contingency Tables
22.4. R Code for the Poisson Exponential Model
22.5. Exercises
Chapter 23. Tools in the Trunk
23.1. Reporting a Bayesian Analysis
23.2. MCMC Burn-in and Thinning
23.3. Functions for Approximating Highest Density Intervals
23.4. Reparameterization of Probability Distributions
References
Index
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