Bayesian statistics for the social sciences
David Kaplan
Bok · Engelsk · 2024
| Omfang | xxi, 250 sider : figurer
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| Utgave | Second edition
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| Opplysninger | Machine generated contents note: I. Foundations -- 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 -- 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 -- 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 -- 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 -- II. Bayesian Model Building -- 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 -- 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 -- 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 -- 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 -- III. Advanced Topics and Methods -- 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 -- 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 -- 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 -- 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 -- List of Abbreviations and Acronyms -- References -- Author Index -- Subject Index -- .. - "Since the publication of the first edition, Bayesian statistics is, arguably, still not the norm in the formal quantitative methods training of social scientists. Typically, the only introduction that a student might have to Bayesian ideas is a brief overview of Bayes' theorem while studying probability in an introductory statistics class. This is not surprising. First, until relatively recently, it was not feasible to conduct statistical modeling from a Bayesian perspective owing to its complexity and lack of available software. Second, Bayesian statistics represents a powerful alternative to frequentist (conventional) statistics and, therefore, can be controversial, especially in the context of null hypothesis significance testing. However, over the last 20 years, or so, considerably progress has been made in the development and application of complex Bayesian statistical methods, due mostly to developments and availability of proprietary and open-source statistical software tools. And, although Bayesian statistics is not quite yet an integral part of the quantitative training of social scientists, there has been increasing interest in the application of Bayesian methods, and it is not unreasonable to say that in terms of theoretical developments and substantive applications, Bayesian statistics has arrived. Because of extensive developments in Bayesian theory and computation since the publication of the first edition of this book, there was a pressing need for a thorough update of the material to reflect new developments in Bayesian methodology and software. The basic foundations of Bayesian statistics remain more or less the same, but this second edition encompasses many new extensions"--
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| Emner | |
| Dewey | |
| ISBN | 9781462553549
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