Bayesian Inference and Mixture Models

9803433Robert E. kass本研究的重点是参考贝叶斯方法（由某种形式规则选择先验分布的贝叶斯推理）、混合模型、贝叶斯因子和因果推理，重点是层次模型（包括经典混合模型及其推广）。研究了参数模型和非参数模型或半参数模型。许多结果是通过渐近方法获得的，但“精确”计算（通常通过模拟）也起着重要作用。在本世纪后半叶，简单统计模型的细化一直是该学科的一个主要主题。以前，模式只涉及少量参数，其值是根据观测数据确定的。随着计算能力的提高，涉及更多参数的更复杂的统计模型已成为当前许多统计活动的核心。然而，尽管最近取得了进展，但根本问题依然存在。这项研究的动机部分来自统计遗传学、认知神经科学和犯罪行为研究中的问题。

9803433Robert E. KassThis research is focused on reference Bayesian methods (Bayesian inference with prior distributions chosen by some formal rule), mixture models, Bayes factors, and causal inference, with an emphasis on hierarchical models (including classical mixed models and their generalizations). Both parametric and nonparametric or semiparametric models are studied. Many of the results are obtained by asymptotic methods, but ``exact'' computation (typically via simulation) also play a substantial role.Elaboration of simple statistical models has been a major theme in the discipline in the latter part of this century. Previously, models have involved a small number of parameters, the values of which have been determined from observed data. With increased computing power, more complicated statistical models involving many more parameters have become central to much current statistical activity. Yet, despite recent progress, fundamental issues remain. This research is motivated in part by problems in statistical genetics, cognitive neuroscience, and the study of criminal behavior.