Bayesian Statistics for the Social Sciences

This book has been replaced by Bayesian Statistics for the Social Sciences, Second Edition, ISBN 978-1-4625-5354-9.

ISBN-13: 9781462553549

Media Type: Hardcover

Publisher: Guilford Publications

Publication Date: 11-10-2023

Pages: 250

Product Dimensions: 10.00h x 6.90w x 0.70d

Series: Methodology in the Social Sciences

David Kaplan, PhD, is the Patricia Busk Professor of Quantitative Methods in the Department of Educational Psychology at the University of Wisconsin–Madison and holds affiliate appointments in the University of Wisconsin’s Department of Population Health Sciences, the Center for Demography and Ecology, and the Nelson Institute for Environmental Studies. Dr. Kaplan’s research focuses on the development of Bayesian statistical methods for education research. His work on these topics is directed toward applications to large-scale cross-sectional and longitudinal survey designs. He has been actively involved in the OECD Program for International Student Assessment (PISA), serving on its Technical Advisory Group from 2005 to 2009 and its Questionnaire Expert Group from 2004 to the present, and chairing the Questionnaire Expert Group for PISA 2015. He also serves on the Design and Analysis Committee and the Questionnaire Standing Committee for the National Assessment of Educational Progress. Dr. Kaplan is an elected member of the National Academy of Education and former chair of its Research Advisory Committee, president (2023–2024) of the Psychometric Society, and past president of the Society for Multivariate Experimental Psychology. He is a fellow of the American Psychological Association (Division 5), a former visiting fellow at the Luxembourg Institute for Social and Economic Research, a former Jeanne Griffith Fellow at the National Center for Education Statistics, and a current fellow at the Leibniz Institute for Educational Trajectories in Bamberg, Germany. He is a recipient of the Samuel J. Messick Distinguished Scientific Contributions Award from the American Psychological Association (Division 5), the Alexander von Humboldt Research Award, and the Hilldale Award for the Social Sciences from the University of Wisconsin–Madison. Dr. Kaplan was the Johann von Spix International Visiting Professor at the Universität Bamberg and the Max Kade Visiting Professor at the Universität Heidelberg, both in Germany, and is currently International Guest Professor at the Universität Heidelberg.

Table of Contents

I. Foundations of Bayesian Statistics
1. Probability Concepts and Bayes' Theorem
1.1. Relevant Probability Axioms
1.1.1. Probability as Long-Run Frequency
1.1.2. The Kolmogorov Axioms of Probability
1.1.3. The Rényi Axioms of Probability
1.1.4. Bayes' Theorem
1.1.5. Epistemic Probability
1.1.6. Coherence
1.2. Summary
1.3. Suggested Readings
2. Statistical Elements of Bayes' Theorem
2.1. The Assumption of Exchangeability
2.2. The Prior Distribution
2.2.1. Noninformative Priors
2.2.2 .Informative Priors
2.3. Likelihood
2.3.1. The Law of Likelihood
2.4. The Posterior Distribution
2.5. The Bayesian Central Limit Theorem and Bayesian Shrinkage
2.6. Summary
2.7. Suggested Readings
2.8. Appendix 2.1. Derivation of Jeffreys' Prior
3. Common Probability Distributions
3.1. The Normal Distribution
3.1.1. The Conjugate Prior for the Normal Distribution
3.2. The Uniform Distribution
3.2.1. The Uniform Distribution as a Noninformative Prior
3.3. The Poisson Distribution
3.3.1. The Gamma Density: Conjugate Prior for the Poisson Distribution
3.4. The Binomial Distribution
3.4.1. The Beta Distribution: Conjugate Prior for the Binomial Distribution
3.5. The Multinomial Distribution
3.5.1. The Dirichlet Distribution: Conjugate Prior for the Multinomial Distribution
3.6. The Wishart Distribution
3.6.1. The Inverse-Wishart Distribution: Conjugate Prior for the Wishart Distribution
3.7. Summary
3.8. Suggested Readings
3.9. 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
4.3. The Gibbs Sampler
4.4. Convergence Diagnostics
4.5. Summary
4.6. Suggested Readings
4.7. Appendix 4.1. R Code for Chapter 4
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
5.2.1. Interval Summaries of the Posterior Distribution
5.3. Bayesian Model Evaluation and Comparison
5.3.1. Posterior Predictive Checks
5.3.2. Bayes Factors
5.3.3. The Bayesian Information Criterion
5.3.4. The Deviance Information Criterion
5.4. Bayesian Model Averaging
5.4.1 Occam's Window
5.4.2. Markov Chain Monte Carlo Model Composition
5.5. Summary
5.6. Suggested Readings
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
6.3.1. Noninformative Priors in the Linear Regression Model
6.3.2. Informative Conjugate Priors
6.4. Bayesian Generalized Linear Models
6.4.1. The Link Function
6.4.2. The Logit-Link Function for Logistic and Multinomial Models
6.5 Summary
6.6 Suggested Readings
6.7. 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
7.2.1. Listwise Deletion
7.2.2. Pairwise Deletion
7.3. Single Imputation Methods
7.3.1. Mean Imputation
7.3.2. Regression Imputation
7.3.3. Stochastic Regression Imputation
7.3.4. Hot-Deck Imputation
7.3.5. Predictive Mean Matching
7.4. Bayesian Methods of Multiple Imputation
7.4.1. Data Augmentation
7.4.2. Chained Equations
7.4.3. EM Bootstrap: A Hybrid Bayesian/Frequentist Method
7.4.4. Bayesian Bootstrap Predictive Mean Matching
7.5. Summary
7.6. Suggested Readings
7.7. Appendix 7.1. R Code for Chapter 7
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
8.4. Summary
8.5. Suggested Readings
8.6. 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
9.1.1. Conjugate Priors for CFA Model Parameters
9.2. Bayesian SEM
9.2.1. Conjugate Priors for SEM Parameters
9.2.2. MCMC Sampling for Bayesian SEM
9.3. Bayesian Multilevel SEM
9.4. Bayesian Growth Curve Modeling
9.5. Bayesian Models for Categorical Latent Variables
9.5.1. Mixture Model Specification
9.5.2. Bayesian Mixture Models
9.6. Summary
9.7. Suggested Readings
9.8. 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
10.1.1. Conditioning on Data
10.1.2. Inferences Based on Data Actually Observed
10.1.3. Quantifying Evidence
10.1.4. Summarizing the Bayesian Advantage
10.2. Subjective Bayes
10.3. Objective Bayes
10.4. Final Thoughts: A Call for Evidence-Base Subjective Bayes
References
Index
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