Bridging the gap between traditional classical statistics and a Bayesian approach, David Kaplan provides readers with the concepts and practical skills they need to apply Bayesian methodologies to their data analysis problems. Part I addresses the elements of Bayesian inference, including exchangeability, likelihood, prior/posterior distributions, and the Bayesian central limit theorem. Part II covers Bayesian hypothesis testing, model building, and linear regression analysis, carefully explaining the differences between the Bayesian and frequentist approaches. Part III extends Bayesian statistics to multilevel modeling and modeling for continuous and categorical latent variables. Kaplan closes with a discussion of philosophical issues and argues for an "evidence-based" framework for the practice of Bayesian statistics.
Useful features for teaching or self-study:
*Includes worked-through, substantive examples, using large-scale educational and social science databases, such as PISA (Program for International Student Assessment) and the LSAY (Longitudinal Study of American Youth).
*Utilizes open-source R software programs available on CRAN (such as MCMCpack and rjags); readers do not have to master the R language and can easily adapt the example programs to fit individual needs.
*Shows readers how to carefully warrant priors on the basis of empirical data.
*Companion website features data and code for the book's examples, plus other r
Chapter
PART I. FOUNDATIONS OF BAYESIAN STATISTICS
1. Probability Concepts and Bayes’ Theorem
1.1. Relevant Probability Axioms
2. Statistical Elements of Bayes’ Theorem
2.1. The Assumption of Exchangeability
2.2. The Prior Distribution
2.4. The Posterior Distribution
2.5. The Bayesian Central Limit Theorem and Bayesian Shrinkage
APPENDIX 2.1. DERIVATION OF JEFFREYS’ PRIOR
3. Common Probability Distributions
3.1. The Normal Distribution
3.2. The Uniform Distribution
3.3. The Poisson Distribution
3.4. The Binomial Distribution
3.5. The Multinomial Distribution
3.6. The Wishart Distribution
APPENDIX 3.1. R CODE FOR CHAPTER 3
4. Markov Chain Monte Carlo Sampling
4.1. Basic Ideas of MCMC Sampling
4.2. The Metropolis–Hastings Algorithm
4.4. Convergence Diagnostics
APPENDIX 4.1. R CODE FOR CHAPTER 4
PART II. TOPICS IN BAYESIAN MODELING
5. Bayesian Hypothesis Testing
5.1. Setting the Stage: The Classical Approach to Hypothesis Testing and Its Limitations
5.2. Point Estimates of the Posterior Distribution
5.3. Bayesian Model Evaluation and Comparison
5.4. Bayesian Model Averaging
6. Bayesian Linear and Generalized Linear Models
6.1. A Motivating Example
6.2. The Normal Linear Regression Model
6.3. The Bayesian Linear Regression Model
6.4. Bayesian Generalized Linear Models
APPENDIX 6.1. R CODE FOR CHAPTER 6
7. Missing Data from a Bayesian Perspective
7.1. A Nomenclature for Missing Data
7.2. Ad Hoc Deletion Methods for Handling Missing Data
7.3. Single Imputation Methods
7.4. Bayesian Methods of Multiple Imputation
APPENDIX 7.1. R CODE FOR CHAPTER 7
PART III. ADVANCED BAYESIAN MODELING METHODS
8. Bayesian Multilevel Modeling
8.1. Bayesian Random Effects Analysis of Variance
8.2. Revisiting Exchangeability
8.3. Bayesian Multilevel Regression
APPENDIX 8.1. R CODE FOR CHAPTER 8
9. Bayesian Modeling for Continuous and Categorical Latent Variables
9.1. Bayesian Estimation of the CFA Model
9.3. Bayesian Multilevel SEM
9.4. Bayesian Growth Curve Modeling
9.5. Bayesian Models for Categorical Latent Variables
APPENDIX 9.1. “rjags” CODE FOR CHAPTER 9
10. Philosophical Debates in Bayesian Statistical Inference
10.1. A Summary of the Bayesian versus Frequentist Schools of Statistics
10.4. Final Thoughts: A Call for Evidence-Based Subjective Bayes
Bayesian Statistics for the Social Sciences
( Methodology in the Social Sciences )
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