Bayesian, Empirical Likelihood and Counting Process Methods for Semiparametric Models

本项目旨在提高半参数模型在天气预报、海洋环流和生物医学应用中的应用范围。贝叶斯，经验似然，计数过程和蒙特卡罗方法的合成用于推进这些领域的统计方法。五个具体的主题进行了研究：贝叶斯单指数模型，贝叶斯反演的海洋环流数据，经验似然方法的治疗比较，测试标记特定的危害和累积发病率函数，协变量选择半参数风险函数回归模型。该项目的初始阶段的动机是天气预测问题，并引入贝叶斯方法的单指数模型，将一些频率的方法，以及有用的先验信息，到推理机。接下来，贝叶斯反演方法的海洋环流反问题的开发，这种方法在其他不适定的反问题的成功和流行的动机。鉴于对生物医学应用，经验的可能性为基础的方法比较两个或两个以上的治疗进行了研究。介绍了一种新的比较标记特异性危险函数的方法，该方法可用于分析艾滋病临床试验中收集的HIV基因数据和评估HIV疫苗的有效性。最后，在一类灵活的新的半参数风险函数回归模型的协变量的最佳子集的模型选择程序。

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.