Mathematical Sciences: Bayesian Inference and Computing

点击翻译按钮获取中文摘要

Tools will be developed for assessing sensitivity of results to assumptions about the prior probability distribution (which represents knowledge gained from sources other than the data being analyzed). A deeper understanding of the role of parameterization of statistical models will be gained through the development of diagnostics for the detection of a poor approximation by a Normal distribution to another distribution. The focus will be the approximation of the posterior distribution which is the basis for inference in a Bayesian analysis. Appropriate numerical integration strategies will be incorporated in a computing environment for Bayesian analysis. Further work will be carried out on asymptotic Bayesian inference for nonparametric problems in which the assumptions of the statistical model are greatly weakened.