Bayesian, Empirical Likelihood and Counting Process Methods for Semiparametric Models

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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.