Informed Proposal Monte Carlo

TL;DR

This paper discusses how incorporating problem-specific information, especially via physics-based models, can significantly improve the efficiency of Markov Chain Monte Carlo methods for solving complex inverse problems.

Contribution

It demonstrates that using informed proposal distributions based on approximate physics models enhances MCMC sampling efficiency in high-dimensional inverse scattering problems.

Findings

Informed proposals improve sampling efficiency.

Physics-based models guide better proposal distributions.

Application to nonlinear inverse scattering shows significant gains.

Abstract

Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a consequence of the the No-Free-Lunch Theorem, the only way we can ensure a significantly better performance of search and sampling algorithms is to build in as much information about the problem as possible. In the special case of Markov Chain Monte Carlo sampling (MCMC) we review how this is done through the choice of proposal distribution, and we show how this way of adding more information about the problem can be made particularly efficient when based on an approximate physics model of the problem. A highly nonlinear inverse scattering problem with a high-dimensional model space serves as an illustration of the gain of efficiency through this approach.