Bayesian Mosaic: Parallelizable Composite Posterior

TL;DR

Bayesian mosaic introduces a parallelizable composite posterior method for scalable Bayesian inference on multivariate discrete data, leveraging marginal densities to enable efficient, independent sampling and improved scalability over traditional MCMC methods.

Contribution

It presents a novel Bayesian mosaic approach that allows parallel sampling using marginal densities, offering scalability and efficiency improvements over existing MCMC techniques.

Findings

Bayesian mosaic achieves consistent and asymptotically normal estimates.

Sampling from Bayesian mosaic is more scalable than traditional DA-MCMC.

Method performs well in simulation and real citation count data analysis.

Abstract

This paper proposes Bayesian mosaic, a parallelizable composite posterior, for scalable Bayesian inference on a broad class of multivariate discrete data models. Sampling is embarrassingly parallel since Bayesian mosaic is a multiplication of component posteriors that can be independently sampled from. Analogous to composite likelihood methods, these component posteriors are based on univariate or bivariate marginal densities. Utilizing the fact that the score functions of these densities are unbiased, we show that Bayesian mosaic is consistent and asymptotically normal under mild conditions. Since the evaluation of univariate or bivariate marginal densities can rely on numerical integration, sampling from Bayesian mosaic bypasses the traditional data augmented Markov chain Monte Carlo (DA-MCMC) method, which has a provably slow mixing rate when data are imbalanced. Moreover, we show that sampling from Bayesian mosaic has better scalability to large sample size than DA-MCMC. The method is evaluated via simulation studies and an application on a citation count dataset.