book

Doing Bayesian Data Analysis

Name: Doing Bayesian Data Analysis
Author: John Kruschke
ISBN: 9780123814869

by John Kruschke

November 2010

Beginner to intermediate

672 pages

19h 28m

English

Academic Press

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Cover image
Title page
Table of Contents
Copyright
Dedication
Chapter 1. This Book’s Organization
1.1 Real People can Read This Book1.2 Prerequisites1.3 The Organization of This Book1.4 Gimme Feedback (Be Polite)1.5 Acknowledgments
Part 1: The Basics: Parameters, Probability, Bayes’ Rule, and R
Chapter 2. Introduction
2.1 Models of Observations and Models of Beliefs2.2 Three Goals for Inference from Data2.3 The R Programming Language2.4 Exercises
Chapter 3. What Is This Stuff Called Probability?
3.1 The Set of All Possible Events3.2 Probability: Outside or Inside the Head3.3 Probability Distributions3.4 Two-Way Distributions3.5 R Code3.6 Exercises
Chapter 4. Bayes’ Rule
4.1 Bayes’ Rule4.2 Applied to Models and Data4.3 The Three Goals of Inference4.4 R Code4.5 Exercises

Part 2: All the Fundamentals Applied to Inferring a Binomial Proportion
Chapter 5. Inferring a Binomial Proportion via Exact Mathematical Analysis
5.1 The Likelihood Function: Bernoulli Distribution5.2 A Description of Beliefs: The Beta Distribution5.3 Three Inferential Goals5.4 Summary: How to do Bayesian Inference5.5 R Code5.6 Exercises
Chapter 6. Inferring a Binomial Proportion via Grid Approximation
6.1 Bayes’ Rule for Discrete Values of6.2 Discretizing a Continuous Prior Density6.3 Estimation6.4 Prediction of Subsequent Data6.5 Model Comparison6.6 Summary6.7 R Code6.8 Exercises
Chapter 7. Inferring a Binomial Proportion via the Metropolis Algorithm
7.1 A Simple Case of the Metropolis Algorithm7.2 The Metropolis Algorithm More Generally7.3 From the Sampled Posterior to the Three Goals7.4 MCMC in BUGS7.5 Conclusion7.6 R Code7.7 Exercises
Chapter 8. Inferring Two Binomial Proportions via Gibbs Sampling
8.1 Prior, Likelihood, and Posterior for Two Proportions8.2 The Posterior via Exact Formal Analysis8.3 The Posterior via Grid Approximation8.4 The Posterior via Markov Chain Monte Carlo8.5 Doing it with BUGS8.6 How Different are the Underlying Biases?8.7 Summary8.8 R Code8.9 Exercises
Chapter 9. Bernoulli Likelihood with Hierarchical Prior
9.1 A Single Coin from a Single Mint9.2 Multiple Coins from a Single Mint9.3 Multiple Coins from Multiple Mints9.4 Summary9.5 R Code9.6 Exercises
Chapter 10. Hierarchical Modeling and Model Comparison
10.1 Model Comparison as Hierarchical Modeling10.2 Model Comparison in BUGS10.3 Model Comparison and Nested Models10.4 Review of Hierarchical Framework for Model Comparison10.5 Exercises
Chapter 11. Null Hypothesis Significance Testing
11.1 NHST for the Bias of a Coin11.2 Prior Knowledge about the Coin11.3 Confidence Interval and Highest Density Interval11.4 Multiple Comparisons11.5 What a Sampling Distribution is Good for11.6 Exercises
Chapter 12. Bayesian Approaches to Testing a Point (“Null”)Hypothesis
12.1 The Estimation (Single Prior) Approach12.2 The Model-Comparison (Two-Prior) Approach12.3 Estimation or Model Comparison?12.4 R Code12.5 Exercises
Chapter 13. Goals, Power, and Sample Size
13.1 The Will to Power13.2 Sample Size for a Single Coin13.3 Sample Size for Multiple Mints13.4 Power: Prospective, Retrospective, and Replication13.5 The Importance of Planning13.6 R Code13.7 Exercises
Part 3: Applied to the Generalized Linear Model
Chapter 14. Overview of the Generalized Linear Model
14.1 The Generalized Linear Model (GLM)14.2 Cases of the GLM14.3 Exercises
Chapter 15. Metric Predicted Variable on a Single Group
15.1 Estimating the Mean and Precision of a Normal Likelihood15.2 Repeated Measures and Individual Differences15.3 Summary15.4 R Code15.5 Exercises
Chapter 16. Metric Predicted Variable with One Metric Predictor
16.1 Simple Linear Regression16.2 Outliers and Robust Regression16.3 Simple Linear Regression with Repeated Measures16.4 Summary16.5 R Code16.6 Exercises
Chapter 17. Metric Predicted Variable with Multiple Metric Predictors
17.1 Multiple Linear Regression17.2 Hyperpriors and Shrinkage of Regression Coefficients17.3 Multiplicative Interaction of Metric Predictors17.4 Which Predictors should be Included?17.5 R Code17.6 Exercises
Chapter 18. Metric Predicted Variable with One Nominal Predictor
18.1 Bayesian Oneway ANOVA18.2 Multiple Comparisons18.3 Two-Group Bayesian ANOVA and the NHST t Test18.4 R Code18.5 Exercises
Chapter 19. Metric Predicted Variable with Multiple Nominal Predictors
19.1 Bayesian Multifactor ANOVA19.2 Repeated Measures, a.k.a. Within-Subject Designs19.3 R Code19.4 Exercises
Chapter 20. Dichotomous Predicted Variable
20.1 Logistic Regression20.2 Interaction of Predictors in Logistic Regression20.3 Logistic ANOVA20.4 Summary20.5 R Code20.6 Exercises
Chapter 21. Ordinal Predicted Variable
21.1 Ordinal Probit Regression21.2 Some Examples21.3 Interaction21.4 Relation to Linear and Logistic Regression21.5 R Code21.6 Exercises
Chapter 22. Contingency Table Analysis
22.1 Poisson Exponential ANOVA22.2 Examples22.3 Log Linear Models for Contingency Tables22.4 R Code for the Poisson Exponential Model22.5 Exercises
Chapter 23. Tools in the Trunk
23.1 Reporting a Bayesian Analysis23.2 MCMC Burn-in and Thinning23.3 Functions for Approximating Highest Density Intervals23.4 Reparameterization of Probability Distributions
Index

Content preview from Doing Bayesian Data Analysis

Chapter 21 Ordinal Predicted Variable

21.1 Ordinal Probit Regression

21.1.1 What the Data Look Like

21.1.2 The Mapping from Metric x to Ordinal y

21.1.3 The Parameters and Their Priors

21.1.4 Standardizing for MCMC Efficiency

21.1.5 Posterior Prediction

21.2 Some Examples

21.2.1 Why Are Some Thresholds Outside the Data?

21.3 Interaction

21.4 Relation to Linear and Logistic Regression

21.5 R Code

21.6 Exercises

The winner is first, and that’s all that he knows, whether

Won by a mile or won by a nose. But

Second recalls every inch of that distance, in

Vivid detail and with haunting persistence.

Very often the predicted variable is ordinal, such as a rating on a scale from 1 to 5. Rate how much you agree with this statement: “Bayesian methods ...

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Doing Bayesian Data Analysis

by John Kruschke

Chapter 21

Ordinal Predicted Variable

Contents

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