Mathematical Sciences: Bayesian Nonparametric Methods and Model Selection

建议：DMS 9504478 PI：普鲁斯霍坦研究所：威斯康星医学院标题：贝叶斯非参数方法和模型选择摘要：这项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，研究的重点是(I)累积风险函数的Beta过程模型和一些伴随的马尔可夫链模型，(Ii)使用扩展Gamma过程的风险率模型，(Iii)具有风险率和累积风险先验的Cox比例风险回归模型，(Iv)Cox回归中的变量选择问题，以及(V)单峰分布模型。在所有情况下，重点都放在可以开发可实现的计算算法的先验上。随着硬件和软件的最新发展，高速计算机模拟技术使克服贝叶斯统计方法的计算问题成为可能，而贝叶斯统计方法几十年来一直被许多著名的理论家从基础上倡导。该项目的研究集中于在生存分析领域进一步推广这种方法。生存数据的统计分析起源于工业中产品可靠性和医学干预后患者生存的应用，事实证明，生存数据的统计分析在评估新材料、新制造方法和新医疗程序方面具有价值。研究人员研究和实施用于分析此类应用领域中产生的数据的改进技术。

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.