Statistical Inferences and Markov Chains, Admissibility, and Strong Inconsistency

DMS 96-26601伊顿 这项研究涉及统计推断的评价 其被表示为数据相关的概率分布。 特别感兴趣的推论包括后验和后验 分布和预测分布， 不适当的先验分布加上正式的应用程序 贝叶斯定理关于可否受理的问题 推理导致了新的和强大的发展 技术基于问题之间的基本联系， 统计决策理论与递归/瞬时问题 涉及对称马尔可夫链。这种基本的联系是 在这项研究中进一步发展沿着与有点结盟 推论的不一致性。应用这种 研究包括评估和改进推理 技术在高维模型，如那些出现 在大规模的环境模型和那些试图描述 全球变化 %%% 许多统计问题，如环境统计中出现的问题， 研究，涉及同时描述和/或同时 许多变量的预测。在这种情况下，人们常常会说， “高维问题”。这项研究涉及的建设， 相关统计方法的评价和比较 在这些高维问题中。最近的事态发展表明 在这项研究中出现的问题，令人惊讶的是， 与某些问题密切相关，这些问题出现在一个看似 不相关的概率。这种联系保证会产生 在实践和理论问题上都有令人振奋的新见解 涉及高维问题。 ***

DMS 96-26601 Eaton This research involves the evaluation of statistical inferences which are expressed as data dependent probability distributions. Inferences of particular interest include both posterior distributions and predictive distributions which are derived from improper prior distributions coupled with the formal application of Bayes Theorem. Questions concerning the admissibility of inferences have lead to the development of new and powerful techniques based on a fundamental connection between issues in statistical decision theory and recurrence/transcience issues involving symmetric Markov Chains. This fundamental connection is further developed in this research along with the somewhat allied noton of strong inconsistency for inferences. Applications of this research include the evaluation and improvement of inferential techniques in high dimensional models such as those which arise in large scale environmental models and those attempting to describe global change. %%% Many problems of statistics, such as those which arise in environmental studies, involve the simultaneous description and/or simultaneous prediction of many variables. In such cases, one often speaks of "high dimensional problems". This research involves the construction, evaluation and comparison of statistical methods which are relevant in these high dimensional problems. Recent developments have shown that the problems which arise in this research are, rather surprisingly, closely connected with certain problems which arise in a seemingly unrelated area of probability. This connection promises to yield exciting new insights regarding both practical and theoretical issues involving high dimensional problems. ***