Doing Bayesian data analysis : a tutorial with R, JAGS, and Stan / John K. Kruschke.

Format:

Book

Author/Creator:

Kruschke, John K., author.

Language:

English

Physical Description:

1 online resource (xii, 759 pages ) illustrations

Edition:

2nd ed.

Place of Publication:

Amsterdam : Academic Press is an imprint of Elsevier, [2015]

System Details:

text file

Summary:

Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan, Second Edition provides an accessible approach for conducting Bayesian data analysis, as material is explained clearly with concrete examples. Included are step-by-step instructions on how to carry out Bayesian data analyses in the popular and free software R and WinBugs, as well as new programs in JAGS and Stan. The new programs are designed to be much easier to use than the scripts in the first edition. In particular, there are now compact high-level scripts that make it easy to run the programs on your own data sets.The book is divided into three parts and begins with the basics: models, probability, Bayes' rule, and the R programming language. The discussion then moves to the fundamentals applied to inferring a binomial probability, before concluding with chapters on the generalized linear model. Topics include metric-predicted variable on one or two groups; metric-predicted variable with one metric predictor; metric-predicted variable with multiple metric predictors; metric-predicted variable with one nominal predictor; and metric-predicted variable with multiple nominal predictors. The exercises found in the text have explicit purposes and guidelines for accomplishment.This book is intended for first-year graduate students or advanced undergraduates in statistics, data analysis, psychology, cognitive science, social sciences, clinical sciences, and consumer sciences in business.- Accessible, including the basics of essential concepts of probability and random sampling- Examples with R programming language and JAGS software- 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)- Coverage of experiment planning- R and JAGS computer programming code on website- Exercises have explicit purposes and guidelines for accomplishment- Provides step-by-step instructions on how to conduct Bayesian data analyses in the popular and free software R and WinBugs

Contents:

Front Cover

Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan

Copyright

Dedication

Contents

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

1.1 Real People Can Read This Book

1.1.1 Prerequisites

1.2 What's in This Book

1.2.1 You're busy. What's the least you can read?

1.2.2 You're really busy! Isn't there even less you can read?

1.2.3 You want to enjoy the view a little longer. But not too much longer

1.2.4 If you just gotta reject a null hypothesis…

1.2.5 Where's the equivalent of traditional test X 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

Chapter 2: Introduction: Credibility, Models, and Parameters

2.1 Bayesian Inference Is Reallocation of CredibilityAcross Possibilities

2.1.1 Data are noisy and inferences are probabilistic

2.2 Possibilities Are Parameter Values in Descriptive Models

2.3 The Steps of Bayesian Data Analysis

2.3.1 Data analysis without parametric models?

2.4 Exercises

Chapter 3: The R Programming Language

3.1 Get the Software

3.1.1 A look at RStudio

3.2 A Simple Example of R in Action

3.2.1 Get the programs used with this book

3.3 Basic Commands and Operators in R

3.3.1 Getting help in R

3.3.2 Arithmetic and logical operators

3.3.3 Assignment, relational operators, and tests of equality

3.4 Variable Types

3.4.1 Vector

3.4.1.1 The combine function

3.4.1.2 Component-by-component vector operations

3.4.1.3 The colon operator and sequence function

3.4.1.4 The replicate function

3.4.1.5 Getting at elements of a vector

3.4.2 Factor

3.4.3 Matrix and array

3.4.4 List and data frame

3.5 Loading and Saving Data

3.5.1 The read.csv and read.table functions.

3.5.2 Saving data from R

3.6 Some Utility Functions

3.7 Programming in R

3.7.1 Variable names in R

3.7.2 Running a program

3.7.3 Programming a function

3.7.4 Conditions and loops

3.7.5 Measuring processing time

3.7.6 Debugging

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

4.1.1 Coin flips: Why you should care

4.2 Probability: Outside or Inside the Head

4.2.1 Outside the head: Long-run relative frequency

4.2.1.1 Simulating a long-run relative frequency

4.2.1.2 Deriving a long-run relative frequency

4.2.2 Inside the head: Subjective belief

4.2.2.1 Calibrating a subjective belief by preferences

4.2.2.2 Describing a subjective belief mathematically

4.2.3 Probabilities assign numbers to possibilities

4.3 Probability Distributions

4.3.1 Discrete distributions: Probability mass

4.3.2 Continuous distributions: Rendezvous with density

4.3.2.1 Properties of probability density functions

4.3.2.2 The normal probability density function

4.3.3 Mean and variance of a distribution

4.3.3.1 Mean as minimized variance

4.3.4 Highest density interval (HDI)

4.4 Two-Way Distributions

4.4.1 Conditional probability

4.4.2 Independence of attributes

4.5 Appendix: R Code for Figure 4.1

4.6 Exercises

Chapter 5: Bayes' Rule

5.1 Bayes' Rule

5.1.1 Derived from definitions of conditional probability

5.1.2 Bayes' rule intuited from a two-way discrete table

5.2 Applied to Parameters and Data

5.2.1 Data-order invariance

5.3 Complete Examples: Estimating Bias in a Coin

5.3.1 Influence of sample size on the posterior

5.3.2 Influence of the prior on the posterior

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

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

6.2.1 Specifying a beta prior

6.3 The Posterior Beta

6.3.1 Posterior is compromise of prior and likelihood

6.4 Examples

6.4.1 Prior knowledge expressed as a beta distribution

6.4.2 Prior knowledge that cannot be expressed as a beta distribution

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

7.2.1 A politician stumbles upon the Metropolis algorithm

7.2.2 A random walk

7.2.3 General properties of a random walk

7.2.4 Why we care

7.2.5 Why it works

7.3 The Metropolis Algorithm More Generally

7.3.1 Metropolis algorithm applied to Bernoulli likelihood and beta prior

7.3.2 Summary of Metropolis algorithm

7.4 Toward Gibbs Sampling: Estimating Two Coin Biases

7.4.1 Prior, likelihood and posterior for two biases

7.4.2 The posterior via exact formal analysis

7.4.3 The posterior via the Metropolis algorithm

7.4.4 Gibbs sampling

7.4.5 Is there a difference between biases?

7.4.6 Terminology: MCMC

7.5 MCMC Representativeness, Accuracy, and Efficiency

7.5.1 MCMC representativeness

7.5.2 MCMC accuracy

7.5.3 MCMC efficiency

7.6 Summary

7.7 Exercises

Chapter 8: JAGS

8.1 JAGS and its Relation to R

8.2 A Complete Example

8.2.1 Load data

8.2.2 Specify model

8.2.3 Initialize chains

8.2.4 Generate chains

8.2.5 Examine chains

8.2.5.1 The plotPost function.

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

8.6.1 Defining new likelihood functions

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

9.1.1 Posterior via grid approximation

9.2 Multiple Coins from a Single Mint

9.2.1 Posterior via grid approximation

9.2.2 A realistic model with MCMC

9.2.3 Doing it with JAGS

9.2.4 Example: Therapeutic touch

9.3 Shrinkage in Hierarchical Models

9.4 Speeding up JAGS

9.5 Extending the Hierarchy: Subjects Within Categories

9.5.1 Example: Baseball batting abilities by position

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

10.2.1 Solution by formal analysis

10.2.2 Solution by grid approximation

10.3 Solution by MCMC

10.3.1 Nonhierarchical MCMC computation of each model'smarginal likelihood

10.3.1.1 Implementation with JAGS

10.3.2 Hierarchical MCMC computation of relative model probability

10.3.2.1 Using pseudo-priors to reduce autocorrelation

10.3.3 Models with different "noise" distributions in JAGS

10.4 Prediction: Model Averaging

10.5 Model Complexity Naturally Accounted for

10.5.1 Caveats regarding nested model comparison

10.6 Extreme Sensitivity to Prior Distribution

10.6.1 Priors of different models should be equally informed

10.7 Exercises

Chapter 11: Null Hypothesis Significance Testing

11.1 Paved with Good Intentions

11.1.1 Definition of p value

11.1.2 With intention to fix N

11.1.3 With intention to fix z.

11.1.4 With intention to fix duration

11.1.5 With intention to make multiple tests

11.1.6 Soul searching

11.1.7 Bayesian analysis

11.2 Prior Knowledge

11.2.1 NHST analysis

11.2.2 Bayesian analysis

11.2.2.1 Priors are overt and relevant

11.3 Confidence Interval and Highest Density Interval

11.3.1 CI depends on intention

11.3.1.1 CI is not a distribution

11.3.2 Bayesian HDI

11.4 Multiple Comparisons

11.4.1 NHST correction for experimentwise error

11.4.2 Just one Bayesian posterior no matter how you look at it

11.4.3 How Bayesian analysis mitigates false alarms

11.5 What a Sampling Distribution Is Good For

11.5.1 Planning an experiment

11.5.2 Exploring model predictions (posterior predictive check)

11.6 Exercises

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

12.1 The Estimation Approach

12.1.1 Region of practical equivalence

12.1.2 Some examples

12.1.2.1 Differences of correlated parameters

12.1.2.2 Why HDI and not equal-tailed interval?

12.2 The Model-Comparison Approach

12.2.1 Is a coin fair or not?

12.2.1.1 Bayes' factor can accept null with poor precision

12.2.2 Are different groups equal or not?

12.2.2.1 Model specification in JAGS

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

13.1.1 Goals and obstacles

13.1.2 Power

13.1.3 Sample size

13.1.4 Other expressions of goals

13.2 Computing Power and Sample Size

13.2.1 When the goal is to exclude a null value

13.2.2 Formal solution and implementation in R

13.2.3 When the goal is precision

13.2.4 Monte Carlo approximation of power

13.2.5 Power from idealized or actual data.

13.3 Sequential Testing and the Goal of Precision.

ISBN:

9780124059160

0124059163

9780124058880

0124058884

OCLC:

1102470196