Bayesian, Empirical Likelihood and Counting Process Methods for Semiparametric Models

本项目旨在扩大半参数模式在天气预报、海洋环流和生物医学应用中的应用范围。综合使用贝叶斯方法、经验似然方法、计数过程方法和蒙特卡罗方法来推进这些领域的统计方法。研究了五个具体主题：贝叶斯单指数模型、海洋环流数据的贝叶斯倒置、用于处理比较的经验似然方法、特定于标记的危害和累积关联函数的检验、以及半参数风险函数回归模型的协变量选择。该项目的初始阶段是由天气预报问题引起的，并引入了用于单指数模型的贝叶斯方法，将一些频率方法以及有用的先验信息纳入到推理机中。其次，根据贝叶斯反问题在其他不适定反问题中的成功和流行，发展了一种用于海洋环流反问题的贝叶斯反问题方法。着眼于生物医学应用，研究了用于比较两个或更多治疗的基于经验似然的方法。介绍了一种比较标记特定危险函数的新方法，该方法可用于艾滋病临床试验中收集的HIV基因数据的分析和HIV疫苗效果的评估。最后，给出了在一类灵活的半参数风险函数回归模型中寻找最佳协变量子集的模型选择方法。

AbstractDMS-0204688PI: Ian McKeagueThis project aims to enhance the scope of semiparametric models for use in weather prediction, ocean circulation and biomedical applications. A synthesis of Bayesian, empirical likelihood, counting process and Monte Carlo methods is used to advance statistical methodology in these areas. Five specific topics are investigated: Bayesian single-index models, Bayesian inversion of ocean circulation data, empirical likelihood methods for treatment comparisons, tests for mark-specific hazards and cumulative incidence functions, and covariate selection for semiparametric hazard function regression models. The initial phase of the project is motivated by a weather prediction problem and introduces Bayesian methodology for single-index models, incorporating some frequentist methods, as well as useful prior information, into the inference machinery. Next, a Bayesian inversion approach for the ocean circulation inverse problem is developed, motivated by the success and popularity of this approach in other ill-posed inverse problems. With a view towards biomedical applications, empirical likelihood based methods for comparing two or more treatments are studied. A new approach for comparing mark-specific hazard functions, which is useful for the analysis of HIV genetic data collected in AIDS clinical trials and the assessment of HIV vaccine efficacy, is introduced. Finally, a model selection procedure for finding the best subset of covariates in a flexible new class of semiparametric hazard function regression model is developed.