Bayesian statistics: an introduction, Volume 2
This volume provides full coverage of Bayesian statistics--perhaps the only fully self-consistent approach in statistics. The book furnishes an understandable treatment of the basic concepts and gives the reader useful information on where and why this somewhat controversial approach differs from "classical" statistics. The appendices include useful tables that are not readily available in other references. The book is based on a a highly successful lecture series for advanced undergraduates and fills a need for a text that is never too elemental nor too technical.
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Exercises on Chapter 1
Some Other Common Distributions
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approximation argument Bayes factor beta distribution binomial distribution bivariate Cauchy distribution chi-squared distribution classical statistician classical statistics conjugate family conjugate prior consider constant corresponding defined degrees of freedom denoted density function depends discrete distribution function elementary event estimate example follows HDRs for log hence implies independent integral interval inverse chi-squared distribution Jeffreys known likelihood function likelihood principle loss function mean and variance median method mode normal distribution Normal mean normal prior normal variance notation null hypothesis observations P-value Pareto distribution particular point null Poisson distribution possible posterior density posterior distribution posterior mean posterior probability predictive distribution prior beliefs prior density prior distribution prior information problem random variable reasonable reference prior sample sometimes standard deviation stopping rule sufficiency principle sufficient statistic Suppose Table A.5—continued Theorem theory tion uniform distribution uniform prior unknown parameter usually variance both unknown vector write