A0331
Title: Bayesian mixture models for histograms: With applications to large datasets
Authors: Richard Warr - Brigham Young University (United States) [presenting]
Abstract: It is not uncommon for privacy or summarization purposes to receive data in a table or in histogram format with bins and associated frequencies. A method that fits a mixture distribution to model the probability density function of the underlying population is presented. The focus is on a mixture of normal distributions, however the method could be generalized to mixtures of other distributions. A prior is placed on the number of mixture components, which could be finite or countably infinite and inference is obtained using reversible jump MCMC. The attractive properties of the method are demonstrated, and they show a great deal of promise for modeling large data problems using a Bayesian nonparametric approach. Additionally, multiple histograms are considered, and those are clustered using the Dirichlet process. This clustering allows for the sharing of information between populations and provides a posterior probability of homogeneity between populations.
