Bayesian statistics: principles, models, and applications
An introduction to Bayesian statistics, with emphasis on interpretation of theory, and application of Bayesian ideas to practical problems. First part covers basic issues and principles, such as subjective probability, Bayesian inference and decision making, the likelihood principle, predictivism, and numerical methods of approximating posterior distributions, and includes a listing of Bayesian computer programs. Second part is devoted to models and applications, including univariate and multivariate regression models, the general linear model, Bayesian classification and discrimination, and a case study of how disputed authorship of some of the Federalist Papers was resolved via Bayesian analysis. Includes biographical material on Thomas Bayes, and a reproduction of Bayes's original essay. Contains exercises.
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Approximations Numerical Methods
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Applications approximation assess assume axiom system Bayes estimator Bayesian analysis Bayesian estimator Bayesian inference Bernoulli binomial Chapter coefficients coin conjugate prior credibility interval defective degree of belief discussion disputed authorship equal essay event has happened example experiment fail q Figure Finetti Finetti's theorem FORTRAN given he/she hyperparameters hypothesis improper prior independent integrals Laplace large samples likelihood function likelihood principle Lindley linear MANOVA marginal posterior density mathematical matrix methods multivariate natural conjugate prior normal Note nuclear observed odds ratio parameters posterior distribution posterior inferences posterior mean posterior odds ratio posterior probability predictive density predictive distribution prior beliefs prior density prior distribution prior probability probability mass function problem procedures Program name Programming language proposition q trials random variables reason Renyi result Section single trial Statistical Inference subjective probability Suppose theory Thomas Bayes tion univariate vague prior variance vector Wherefore Zellner