|
Abstract:
|
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.
|
