Inference and rare event simulation for stopped Markov processes via reverse-time sequential Monte Carlo

TL;DR

This paper introduces a reverse-time sequential Monte Carlo method for efficiently estimating rare event probabilities in Markov processes, reducing high-dimensional sampling difficulties by approximating Green's function ratios.

Contribution

The paper develops a novel reverse-time SMC algorithm that simplifies proposal design in high dimensions using Green's function ratio approximations.

Findings

Effective in estimating overflow probabilities in queueing models

Accurate in modeling diffusion corridor crossing probabilities

Useful for locating initial infection sources in epidemic networks

Abstract

We present a sequential Monte Carlo algorithm for Markov chain trajectories with proposals constructed in reverse time, which is advantageous when paths are conditioned to end in a rare set. The reverse time proposal distribution is constructed by approximating the ratio of Green's functions in Nagasawa's formula. Conditioning arguments can be used to interpret these ratios as low-dimensional conditional sampling distributions of some coordinates of the process given the others. Hence the difficulty in designing SMC proposals in high dimension is greatly reduced. We illustrate our method on estimating an overflow probability in a queueing model, the probability that a diffusion follows a narrowing corridor, and the initial location of an infection in an epidemic model on a network.