Mathematical Sciences: Bayesian Nonparametric Methods and Model Selection

提案：DMS 9504478 PI：Purushottam Laud机构：威斯康星州医学院标题：贝叶斯非参数方法和模型选择 摘要： 本研究为贝叶斯非参数模型发展了新的统计方法，特别关注生存分析中出现的问题。特别是，调查的重点是（一）贝塔过程模型的累积风险函数和一些随之而来的马尔可夫链模型，（二）风险率模型使用扩展伽马过程，（三）考克斯的比例风险回归模型与先验的风险率和累积风险，（四）在考克斯回归的变量选择的问题，和（五）单峰分布模型。在所有情况下，重点放在先验的可实现的计算算法可以开发。 随着计算机硬件和软件技术的发展，高速计算机仿真技术的出现，使人们可以超越传统的计算机仿真技术， 贝叶斯统计方法中的问题，一直主张对 几十年来，许多领先的理论家提出了基本的理由。该项目的研究集中在生存分析领域进一步推广这种方法。起源于工业中产品可靠性和药物干预后患者生存的应用， 存活数据已证明在评估新材料、新制造方法和新医疗程序方面很有价值。调查员研究和实施用于分析这些应用领域中产生的数据的精细技术。

Proposal: DMS 9504478 PI: Purushottam Laud Institution: Medical College of Wisconsin Title: Bayesian Nonparametric Methods and Model Selection ABSTRACT: This research develops new statistical methods for Bayesian nonparametric models, with special attention to problems arising in survival analysis. In particular, the investigation focuses on (i) Beta process models for the cumulative hazard function and some attendant Markov chain models, (ii) hazard rate models using the Extended Gamma process, (iii) Cox's proportional hazards regression model with priors on hazard rates and cumulative hazards, (iv) the problem of variable selection in Cox regression, and (v) unimodal distribution models. In all cases, emphasis is placed on priors for which implementable computational algorithms can be developed. With the recent developments in hardware and software, high-speed computer simulation technology has made it feasible to surmount the computational problems in Bayesian statistical methods which have been advocated on foundational grounds by many leading theoreticians for decades. The research in this project concentrates on furthering such methods in the area of survival analysis. Originating with applications to product reliability in industry and to patient survival after intervention in medicine, statistical analyses of survival data have proved valuable in evaluating new materials, new manufacturing methods and new medical procedures. The investigator studies and implements refined techniques for the analysis of data arising in such fields of application.