Actions for Statistical inference : an integrated Bayesian
Statistical inference : an integrated Bayesian/likelihood approach / Murray Aitkin
- Author
- Aitkin, Murray A.
- Published
- Boca Raton, FL : Chapman & Hall/CRC, [2010]
- Copyright Date
- ©2010
- Physical Description
- xvii, 236 pages : illustrations ; 25 cm.
- Series
- Contents
- 1. Theories of Statistical Inference -- 1.1. Example -- 1.2. Statistical models -- 1.3. The likelihood function -- 1.4. Theories -- 1.4.1. Pure likelihood theory -- 1.4.2. Bayesian theory -- 1.4.3. Likelihood-based repeated sampling theory -- 1.4.4. "Model-guided" survey sampling theory -- 1.5. Nonmodel-based repeated sampling -- 1.6. Conclusion -- 2. The Integrated Bayes/Likelihood Approach -- 2.1. Introduction -- 2.2. Probability -- 2.3. Prior ignorance -- 2.4. The importance of para metrication -- 2.4.1. Inference about the Binomial N -- 2.4.1.1. Profiting -- 2.4.1.2. Conditioning -- 2.4.2. The effect size -- 2.5. The simple/simple hypothesis testing problem -- 2.5.1. Bayes calibration -- 2.5.2. Frequentist calibration (fixed sample size) -- 2.5.3. Nonfixed error probabilities -- 2.5.4. Frequentist test (sequential sampling) -- 2.5.5. Bayesian interpretation of type I error probabilities -- 2.6. The simple/composite hypothesis testing problem -- 2.6.1. Fixed-sample frequentist analysis -- 2.6.2. Sequential sampling approach -- 2.7. Posterior likelihood approach -- 2.7.1. Large-sample result -- 2.7.2. Strength of support for the null hypothesis -- 2.7.3. Credible intervals for the deviance difference -- 2.8. Bayes factors -- 2.8.1. Difficulties with the Bayes factor -- 2.8.2. Conjugate prior difficulties -- 2.8.3. Stone example -- 2.9. The comparison of unrelated models -- 2.9.1. Large-sample result -- 2.9.2. Bayes factor -- 2.9.3. Example -- 2.9.4. Misleading conclusions from Bayes factors -- 2.9.5. Modified Bayes factors -- 2.10. Example - GHQ score and psychiatric diagnosis -- 3. t-Tests and Normal Variance Tests -- 3.1. One-sample t-test -- 3.1.1. Credible interval -- 3.1.2. Model comparisons -- 3.1.3. Example -- 3.2. Two samples: equal variances -- 3.2.1. Credible interval -- 3.2.2. Model comparisons -- 3.2.3. Example -- 3.3. The two-sample test -- 3.3.1. Informative prior for the effect size -- 3.4. Two samples: different variances -- 3.4.1. Credible interval -- 3.4.2. Model comparison -- 3.4.3. Example -- 3.5. The normal model variance -- 3.5.1. Credible interval -- 3.5.2. Model comparisons -- 3.5.3. Example -- 3.5.4. Marginal and full likelihoods -- 3.6. Variance heterogeneity test -- 3.6.1. Nonrobustness of variance tests -- 4. Unified Analysis of Finite Populations -- 4.1. Sample selection indicators -- 4.2. The Bayesian bootstrap -- 4.2.1. Multinomial model -- 4.2.2. Dirichlet prior -- 4.2.3. Confidence coverage of credible intervals -- 4.2.4. Example - income population -- 4.2.5. Simulation study -- 4.2.6. Extensions of the Bayesian bootstrap -- 4.3. Sampling without replacement -- 4.3.1. Simulation study -- 4.4. Regression models -- 4.4.1. Design-based approach -- 4.4.2. Bayesian bootstrap approach -- 4.4.3. Simulation study -- 4.4.4. Ancillary information -- 4.4.5. Sampling without replacement -- 4.4.6. Simulation study -- 4.5. More general regression models -- 4.6. The multinomial model for multiple populations -- 4.7. Complex sample designs -- 4.7.1. Stratified sampling -- 4.7.2. Cluster sampling -- 4.7.3. Shrinkage estimation -- 4.8. A complex example -- 4.9. Discussion -- 5. Regression and Analysis of Variance -- 5.1. Multiple regression -- 5.2. Nonnested models -- 6. Binomial and Multinomial Data -- 6.1. Single binomial samples -- 6.1.1. Bayes factor -- 6.1.2. Example -- 6.2. Single multinomial samples -- 6.3. Two-way tables for correlated proportions -- 6.3.1. Likelihood -- 6.3.2. Bayes factor -- 6.3.3. Posterior likelihood ratio -- 6.4. Multiple binomial samples -- 6.4.1. A social network table -- 6.4.2. Network model -- 6.4.3. Frequentist analysis -- 6.4.4. Choice of alternative model prior -- 6.4.5. Simulations -- 6.5. Two-way tables for categorical responses - no fixed margins -- 6.5.1. The ECMO study -- 6.5.2. Bayes analysis -- 6.5.3. Multinomial likelihoods -- 6.5.4. Dirichlet prior -- 6.5.5. Simulations -- 6.6. Two-way tables for categorical responses - one fixed margin -- 6.7. Multinomial "nonparametric" analysis -- 7. Goodness of Fit and Model Diagnostics -- 7.1. Frequentist model diagnostics -- 7.2. Bayesian model diagnostics -- 7.3. The posterior predictive distribution -- 7.3.1. Marginalization and model diagnostics -- 7.4. Multinomial deviance computation -- 7.5. Model comparison through posterior deviances -- 7.6. Examples -- 7.6.1. Three binomial models -- 7.6.2. Poisson model -- 7.7. Simulation study -- 7.8. Discussion -- 8. Complex Models -- 8.1. The data augmentation algorithm -- 8.2. Two-level variance component models -- 8.2.1. Two-level fixed effects model -- 8.2.2. Two-level random effects model -- 8.2.3. Posterior inference -- 8.2.4. Likelihood -- 8.2.5. Maximum likelihood estimates -- 8.2.6. Posteriors -- 8.2.7. Box-Tiao example -- 8.3. Test for a zero variance component -- 8.3.1. Alternative tests -- 8.3.2. Generalized linear mixed models -- 8.4. Finite mixtures -- 8.4.1. Example - the galaxy velocity study -- 8.4.2. Data examination -- 8.4.3. Maximum likelihood estimates -- 8.4.4. Bayes analysis -- 8.4.5. Posterior likelihood analysis -- 8.4.6. Simulation studies.
- Summary
- "Filling a gap in current Bayesian theory, Statistical Inference: An Integrated Bayesian/Likelihood Approach presents a unified Bayesian treatment of parameter inference and model comparisons that can be used with simple diffuse prior specifications. This novel approach provides new solutions to difficult model comparison problems and offers direct Bayesian counterparts of frequentist f-tests and other standard statistical methods for hypothesis testing" "After an overview of the competing theories of statistical inference, the book introduces the Bayes/likelihood approach used throughout. It presents Bayesian versions of one- and two-sample Mests, along with the corresponding normal variance tests. The author then thoroughly discusses the use of the multinomial model and noninformative Dirichlet priors in "model-free" or nonparametric Bayesian survey analysis, before covering normal regression and analysis of variance. In the chapter on binomial and multinomial data, he gives alternatives, based on Bayesian analyses, to current frequentist nonparametric methods. The text concludes with new goodness-of-fit methods for assessing parametric models and a discussion of two-level variance component models and finite mixtures Features" "Emphasizing the principles of Bayesian inference and Bayesian model comparison, this book develops a unique methodology for solving challenging inference problems. It also includes a concise review of the various approaches to inference"--BOOK JACKET.
- Subject(s)
- ISBN
- 9781420093438 (hardcover : alk. paper)
1420093436 (hardcover : alk. paper) - Bibliography Note
- Includes bibliographical references and indexes.
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