A method for importance sampling through Markov chain Monte Carlo with post sampling variational estimate

TL;DR

This paper introduces a novel importance sampling technique that combines MCMC sampling with a post-sampling variational estimate to efficiently compute integrals of truncated probability densities.

Contribution

The method uniquely integrates MCMC sampling with a variational approach to estimate normalization constants for truncated densities, improving efficiency.

Findings

Effective in numerical case studies

Handles truncated densities efficiently

Discusses potential enhancements and limitations

Abstract

We propose a method to efficiently integrate truncated probability densities. The method uses Markov chain Monte Carlo method to sample from a probability density matching the function being integrated. The required normalisation or equivalently the result is obtained by constructing a function with known integral, through non-parametric kernel density estimation and variational procedure. The method is demonstrated with numerical case studies. Possible enhancements to the method and limitations are discussed.