Mathematical Sciences: Bayesian Nonparametric Methods and Model Selection

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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.