Transport Reversible Jump Proposals

TL;DR

This paper introduces a novel non-linear transport-based method for reversible jump MCMC proposals, leveraging deep neural network techniques to improve sampling efficiency across complex models.

Contribution

It is the first to apply a transport-based approach using reference distributions for transdimensional jumps in RJMCMC, enhancing acceptance rates and mixing.

Findings

Proposed method achieves higher acceptance rates.

Demonstrated improved mixing in complex models.

Acceptance probability depends only on model probabilities.

Abstract

Reversible jump Markov chain Monte Carlo (RJMCMC) proposals that achieve reasonable acceptance rates and mixing are notoriously difficult to design in most applications. Inspired by recent advances in deep neural network-based normalizing flows and density estimation, we demonstrate an approach to enhance the efficiency of RJMCMC sampling by performing transdimensional jumps involving reference distributions. In contrast to other RJMCMC proposals, the proposed method is the first to apply a non-linear transport-based approach to construct efficient proposals between models with complicated dependency structures. It is shown that, in the setting where exact transports are used, our RJMCMC proposals have the desirable property that the acceptance probability depends only on the model probabilities. Numerical experiments demonstrate the efficacy of the approach.