IID Sampling from Posterior Dirichlet Process Mixtures

06/18/2022
by   Sourabh Bhattacharya, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/27/2020

Comparison of Bayesian Nonparametric Density Estimation Methods

In this paper, we propose a nonparametric Bayesian approach for Lindsey ...
research
12/15/2021

IID Sampling from Doubly Intractable Distributions

Intractable posterior distributions of parameters with intractable norma...
research
03/17/2020

Nearest Neighbor Dirichlet Process

There is a rich literature on Bayesian nonparametric methods for unknown...
research
05/15/2019

Compound Dirichlet Processes

The compound Poisson process and the Dirichlet process are the pillar st...
research
04/08/2013

ClusterCluster: Parallel Markov Chain Monte Carlo for Dirichlet Process Mixtures

The Dirichlet process (DP) is a fundamental mathematical tool for Bayesi...
research
07/13/2021

IID Sampling from Intractable Distributions

We propose a novel methodology for drawing iid realizations from any tar...
research
10/08/2013

Retrieval of Experiments with Sequential Dirichlet Process Mixtures in Model Space

We address the problem of retrieving relevant experiments given a query ...

Please sign up or login with your details

Forgot password? Click here to reset