Bayesian statistics for the social sciences / David Kaplan
- Author
- Kaplan, David, 1955-
- Published
- New York : The Guilford Press, 2014.
- Physical Description
- xviii, 318 pages ; 25 cm.
- Series
- Contents
- Machine generated contents note: 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 Renyi 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 -- 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 -- 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 -- Appendix 4.1 R Code For Chapter 4 -- 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 -- 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 -- Appendix 7.1 R Code For Chapter 7 -- 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 -- 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 -- 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.Quantifring Evidence -- 10.1.4.Summarizing the Bayesian Advantage -- 10.2.Subjective Bayes -- 10.3.Objective Bayes -- 10.4.Final Thoughts: A Call for Evidence-Based Subjective Bayes.
- Summary
- " 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. *Utilizes open-source R software programs available on the 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 resources. "--
- Subject(s)
- ISBN
- 9781462516513 (hardback)
1462516513 (hardback) - Bibliography Note
- Includes bibliographical references and index.
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