Bayesian Statistics for the Social Sciences

Name: Bayesian Statistics for the Social Sciences
Price: 75 USD
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ISBN: 9781462553549

by David Kaplan

2nd Edition

Publisher: The Guilford Press

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Probability & Statistics

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Book Details

Print ISBN	9781462553549
eText ISBN	9781462553556
Publisher	The Guilford Press
Publishing Year	2023
Edition	2nd Edition
Language	English
Pages	250

Bayesian Statistics for the Social Sciences, 2nd Edition, by David Kaplan provides social science researchers with a grounded guide to Bayesian inferential methods. The volume establishes principles of probability theory alongside the specific statistical elements of Bayes' theorem, explaining the practical steps required for obtaining and summarizing posterior distributions in research settings.

The thematic coverage connects probability theory with quantitative estimation practices by examining both frequentist and epistemic probability together with common probability distributions and their respective priors. The text expands into standard regression and structural modeling frameworks, detailing analytical approaches to Bayesian linear regression, generalized linear models, model evaluation and comparison, and Bayesian multilevel modeling.

To support practical quantitative estimation, the publication emphasizes open-source software applications alongside theoretical explanations. Social science researchers are provided with structured opportunities to practice applying these statistical modeling methods in empirical research by working directly with code designed for the RStan software package.

Chapter 1: Probability Concepts and Bayes' Theorem
- • 1.1 Relevant Probability Axioms
- • 1.1.1 The Kolmogorov Axioms of Probability
- • 1.1.2 The Rényi Axioms of Probability
- • 1.2 Frequentist Probability
- • 1.3 Epistemic Probability
- • 1.3.1 Coherence and the Dutch Book
- • 1.3.2 Calibrating Epistemic Probability Assessment
- • 1.4 Bayes' Theorem
- • 1.4.1 The Monty Hall Problem
- • 1.5 Summary
Chapter 2: Statistical Elements of Bayes' Theorem
- • 2.1 Bayes' Theorem Revisited
- • 2.2. Hierarchical Models and Pooling
- • 2.3 The Assumption of Exchangeability
- • 2.4 The Prior Distribution
- • 2.4.1 Non-informative Priors
- • 2.4.2 Jeffreys' Prior
- • 2.4.3 Weakly Informative Priors
- • 2.4.4 Informative Priors
- • 2.4.5 An Aside: Cromwell's Rule
- • 2.5 Likelihood
- • 2.5.1 The Law of Likelihood
- • 2.6 The Posterior Distribution
- • 2.7 The Bayesian Central Limit Theorem and Bayesian Shrinkage
- • 2.8 Summary
Chapter 3: Common Probability Distributions and Their Priors
- • 3.1 The Gaussian Distribution
- • 3.1.1 Mean Unknown, Variance Known: The Gaussian Prior
- • 3.1.2 The Uniform Distribution as a Non-informative Prior
- • 3.1.3 Mean Known, Variance Unknown: The Inverse-Gamma Prior
- • 3.1.4 Mean Known, Variance Unknown: The Half-Cauchy Prior
- • 3.1.5 Jeffreys' Prior for the Gaussian Distribution
- • 3.2 The Poisson Distribution
- • 3.2.1 The Gamma Prior
- • 3.2.2 Jeffreys' Prior for the Poisson Distribution
- • 3.3 The Binomial Distribution
- • 3.3.1 The Beta Prior
- • 3.3.2 Jeffreys' Prior for the Binomial Distribution
- • 3.4 The Multinomial Distribution
- • 3.4.1 The Dirichlet Prior
- • 3.4.2 Jeffreys' Prior for the Multinomial Distribution
- • 3.5 The Inverse-Wishart Distribution
- • 3.6 The LKJ Prior for Correlation Matrices
- • 3.7 Summary
Chapter 4: Obtaining and Summarizing the Posterior Distribution
- • 4.1 Basic Ideas of Markov Chain Monte Carlo Sampling
- • 4.2 The Random Walk Metropolis–Hastings Algorithm
- • 4.3 The Gibbs Sampler
- • 4.4 Hamiltonian Monte Carlo
- • 4.4.1 No-U-Turn (NUTS) Sampler
- • 4.5 Convergence Diagnostics
- • 4.5.1 Trace Plots
- • 4.5.2 Posterior Density Plots
- • 4.5.3 Auto-Correction Plots
- • 4.5.4 Effective Sample Size
- • 4.5.5 Potential Scale Reduction Factor
- • 4.5.6 Possible Error Messages When Using HMC/NUTS
- • 4.6 Summarizing the Posterior Distribution
- • 4.6.1 Point Estimates of the Posterior Distribution
- • 4.6.2 Interval Summaries of the Posterior Distribution
- • 4.7 Introduction to Stan and Example
- • 4.8 An Alternative Algorithm: Variational Bayes
- • 4.8.1 Evidence Lower Bound (ELBO)
- • 4.8.2 Variational Bayes Diagnostics
- • 4.9 Summary
Chapter 5: Bayesian Linear and Generalized Models
- • 5.1 The Bayesian Linear Regression Model
- • 5.1.1 Non-informative Priors in the Linear Regression Model
- • 5.2 Bayesian Generalized Linear Models
- • 5.2.1 The Link Function
- • 5.3 Bayesian Logistic Regression
- • 5.4 Bayesian Multinomial Regression
- • 5.5 Bayesian Poisson Regression
- • 5.6 Bayesian Negative Binomial Regression
- • 5.7 Summary
Chapter 6: Model Evaluation and Comparison
- • 6.1 The Classical Approach to Hypothesis Testing and Its Limitations
- • 6.2 Model Assessment
- • 6.2.1 Prior Predictive Checking
- • 6.2.2 Posterior Predictive Checking
- • 6.3 Model Comparison
- • 6.3.1 Bayes Factors
- • 6.3.2 The Deviance Information Criterion (DIC)
- • 6.3.3 Widely Applicable Information Criterion (WAIC)
- • 6.3.4 Leave-One-Out Cross-Validation
- • 6.3.5 A Comparison of WAIC and LOO
- • 6.4 Summary
Chapter 7: Bayesian Multilevel Modeling
- • 7.1 Revisiting Exchangeability
- • 7.2 Bayesian Random Effects Analysis of Variance
- • 7.3 Bayesian Intercepts as Outcomes Model
- • 7.4 Bayesian Intercepts and Slopes as Outcomes Model
- • 7.5 Summary
Chapter 8: Bayesian Latent Variable Modeling
- • 8.1 Bayesian Estimation for the CFA
- • 8.1.1 Priors for CFA Model Parameters
- • 8.2 Bayesian Latent Class Analysis
- • 8.2.1 The Problem of Label-Switching and a Possible Solution
- • 8.2.2 Comparison of VB to the EM Algorithm
- • 8.3 Summary
Chapter 9: Missing Data From a Bayesian Perspective
- • 9.1 A Nomenclature for Missing Data
- • 9.2 Ad Hoc Deletion Methods for Handling Missing Data
- • 9.2.1 Listwise Deletion
- • 9.2.2 Pairwise Deletion
- • 9.3 Single Imputation Methods
- • 9.3.1 Mean Imputation
- • 9.3.2 Regression Imputation
- • 9.3.3 Stochastic Regression Imputation
- • 9.3.4 Hot Deck Imputation
- • 9.3.5 Predictive Mean Matching
- • 9.4 Bayesian Methods for Multiple Imputation
- • 9.4.1 Data Augmentation
- • 9.4.2 Chained Equations
- • 9.4.3 EM Bootstrap: A Hybrid Bayesian/Frequentist Methods
- • 9.4.4 Bayesian Bootstrap Predictive Mean Matching
- • 9.4.5 Accounting for Imputation Model Uncertainty
- • 9.5 Summary
Chapter 10: Bayesian Variable Selection and Sparsity
- • 10.1 Introduction
- • 10.2 The Ridge Prior
- • 10.3 The Lasso Prior
- • 10.4 The Horseshoe Prior
- • 10.5 Regularized Horseshoe Prior
- • 10.6 Comparison of Regularization Methods
- • 10.6.1 An Aside: The Spike-and-Slab Prior
- • 10.7 Summary
Chapter 11: Model Uncertainty
- • 11.1 Introduction
- • 11.2 Elements of Predictive Modeling
- • 11.2.1 Fixing Notation and Concepts
- • 11.2.2 Utility Functions for Evaluating Predictions
- • 11.3 Bayesian Model Averaging
- • 11.3.1 Statistical Specification of BMA
- • 11.3.2 Computational Considerations
- • 11.3.3 Markov Chain Monte Carlo Model Composition
- • 11.3.4 Parameter and Model Priors
- • 11.3.5 Evaluating BMA Results: Revisiting Scoring Rules
- • 11.4 True Models, Belief Models, and M-Frameworks
- • 11.4.1 Model Averaging in the M-Closed Framework
- • 11.4.2 Model Averaging in the M-Complete Framework
- • 11.4.3 Model Averaging in the M-Open Framework
- • 11.5 Bayesian Stacking
- • 11.5.1 Choice of Stacking Weights
- • 11.6 Summary
Chapter 12: Closing Thoughts
- • 12.1 A Bayesian Workflow for the Social Sciences
- • 12.2 Summarizing the Bayesian Advantage
- • 12.2.1 Coherence
- • 12.2.2 Conditioning on Observed Data
- • 12.2.3 Quantifying Evidence
- • 12.2.4 Validity
- • 12.2.5 Flexibility in Handling Complex Data Structures
- • 12.2.6 Formally Quantifying Uncertainty