Simulation from quasi-stationary distributions on reducible state spaces

TL;DR

This paper develops a Sequential Monte Carlo framework with novel resampling techniques to efficiently simulate quasi-stationary distributions in reducible state spaces, addressing challenges in sampling and eigenvalue estimation.

Contribution

It introduces new resampling methods within SMC to preserve diversity in reducible spaces and proposes an approach to estimate eigenvalues related to QSDs.

Findings

Effective resampling techniques for reducible state spaces

Successful simulation of QSDs using SMC methods

Method for estimating decay parameters and eigenvalues

Abstract

Quasi-stationary distributions (QSDs)arise from stochastic processes that exhibit transient equilibrium behaviour on the way to absorption QSDs are often mathematically intractable and even drawing samples from them is not straightforward. In this paper the framework of Sequential Monte Carlo samplers is utilized to simulate QSDs and several novel resampling techniques are proposed to accommodate models with reducible state spaces, with particular focus on preserving particle diversity on discrete spaces. Finally an approach is considered to estimate eigenvalues associated with QSDs, such as the decay parameter.