Without-replacement sampling for particle methods on finite state spaces

摘要

Combinatorial estimation is a new area of application for sequential Monte Carlo methods. We use ideas from sampling theory to introduce new without-replacement sampling methods in such discrete settings. These without-replacement sampling methods allow the addition of merging steps, which can significantly improve the resulting estimators. We give examples showing the use of the proposed methods in combinatorial rare-event probability estimation and in discrete state-space models.