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Activity Number: 526 - Bayesian Clustering and Variable Selection
Type: Contributed
Date/Time: Wednesday, August 1, 2018 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #330083 Presentation
Title: Nonparametric Mixture Modeling on Constrained Spaces
Author(s): Putu Ayu Sudyanti* and Vinayak P Rao
Companies: Purdue and Purdue University
Keywords: Bayesian nonparametrics; Hierarchical models; MCMC; Mixture Models

We explore challenges in flexibly modeling multi-modal data that exists on constrained spaces. A standard approach to model such data is to apply nonparametric mixture models each of whose components follows an appropriate truncated distribution. Problems arise when the truncation has a complex shape, leading to difficulties in specifying the component distributions, and in evaluating their normalization constants. Example applications with such constraints include crime data in a specific geographical area. Bayesian inference over the parameters of these models results in a posterior distribution that is doubly-intractable. We address this situation via an algorithm based on rejection sampling and data augmentation. We view the truncated distributions as outcomes of a rejection sampling scheme, where proposals are made from a simple distribution, and are rejected if they violate the constraints. Our scheme then resamples the rejected samples in the joint distribution, resulting in a tractable function where standard Markov chain Monte Carlo algorithm can be applied. We show how this can be done efficiently, and also study approximations to this exact algorithm.

Authors who are presenting talks have a * after their name.

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