2022/06/18 by Sourabh Bhattacharya, Bhattacharya, Sourabh
Chemistry · Computer Science · #Bayesian Methods and Mixture Models #Computation (stat.CO) #Diffusion Coefficients in Liquids #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2206.09233
openalex publication_date 2022/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The influence of Dirichlet process mixture is ubiquitous in the Bayesian nonparametrics literature. But sampling from its posterior distribution remains a challenge, despite the advent of various Markov chain Monte Carlo methods. The primary challenge is the infinite-dimensional setup, and even if the infinite-dimensional random measure is integrated out, high-dimensionality and discreteness still remain difficult issues to deal with. In this article, exploiting the key ideas proposed in Bhattacharya (2021b), we propose a novel methodology for drawing iid realizations from posteriors of Dirichlet process mixtures. We focus in particular on the more general and flexible model of Bhattacharya (2008), so that the methods developed here are simply applicable to the traditional Dirichlet process mixture. We illustrate our ideas on the well-known enzyme, acidity and the galaxy datasets, which are usually considered benchmark datasets for mixture applications. Generating 10, 000 iid realizations from the Dirichlet process mixture posterior of Bhattacharya (2008) given these datasets took 19 minutes, 8 minutes and 5 minutes, respectively, in our parallel implementation.