Ph.D. (Doctor of Philosophy)
Department of Mathematical Sciences
Many scientific problems require statistical inference in complex models. Bayesian nonparametric models provide a flexible modeling and inference framework for such problems. There is a substantial literature on Bayesian computational methods for nonparametric models, however, in non-conjugate complex models, they can be difficult or computationally expensive to implement. Approximate Bayesian Computation (ABC) provides a computational framework for inference in difficult and intractable Bayesian models. The idea behind ABC is to provide an approximate posterior inference without evaluating the likelihood function based on samples drawn from the sampling distribution. We develop a methodology for statistical inference in nonparametric Bayesian models based on ABC. We utilize the conditionally independent model structure to address the difficult problem of summary statistic choice in ABC. The developed method is generalized to complex nonlinear Bayesian nonparametric models, including generalized linear mixed models and survival models for recurrent data. We further generalize this approach to Bayesian nonparametric models involving the Pitman-Yor process. The approach is further extended to Bayesian nonparametric models involving the stable distributions which are often intractable due to lack of closed-form expressions. Throughout this dissertation, we illustrate the proposed methods in simulated and real datasets and we compare their performances with preexisting methods.
Paul, Erina, "Approximate Bayesian computation in nonparametric Bayesian models" (2017). Graduate Research Theses & Dissertations. 1509.
ix, 127 pages
Northern Illinois University
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