Posterior exploration for computationally intensive forward models

TL;DR

This paper investigates methods to efficiently explore posterior distributions in Bayesian inverse problems involving costly forward models, using multivariate proposals, single-site updates, and approximate models to enhance MCMC sampling.

Contribution

It introduces strategies combining multivariate proposals and approximate models to improve sampling efficiency in computationally intensive Bayesian inverse problems.

Findings

Multivariate proposals outperform single-site updates in efficiency.

Approximate models significantly speed up MCMC sampling.

Combining proposals with approximations yields better exploration of posteriors.

Abstract

In this chapter, we address the challenge of exploring the posterior distributions of Bayesian inverse problems with computationally intensive forward models. We consider various multivariate proposal distributions, and compare them with single-site Metropolis updates. We show how fast, approximate models can be leveraged to improve the MCMC sampling efficiency.