Generalized Direct Sampling for Hierarchical Bayesian Models

TL;DR

This paper introduces a novel importance sampling-based method for directly sampling from hierarchical Bayesian model posteriors, enabling parallel, independent samples without MCMC drawbacks, and facilitating marginal likelihood computation.

Contribution

It presents a new generalized direct sampling technique that avoids MCMC, applicable to high-dimensional hierarchical models, and capable of estimating marginal likelihoods.

Findings

Samples are independent and can be generated in parallel.

The method is applicable to high-dimensional models with large data sets.

It allows direct computation of marginal likelihoods.

Abstract

We develop a new method to sample from posterior distributions in hierarchical models without using Markov chain Monte Carlo. This method, which is a variant of importance sampling ideas, is generally applicable to high-dimensional models involving large data sets. Samples are independent, so they can be collected in parallel, and we do not need to be concerned with issues like chain convergence and autocorrelation. Additionally, the method can be used to compute marginal likelihoods.