Resampling in conditional SMC algorithms

2026-06-24

AI Summary

This work addresses the challenge of implementing resampling steps in conditional sequential Monte Carlo (CSMC) algorithms, particularly when dealing with complex dependency structures. The authors propose a unified framework that accommodates a wide range of standard and nonstandard resampling schemes—including systematic, adaptive, and chopthin resampling—without requiring strong assumptions such as unbiasedness or exchangeability. By preserving the order of ancestor indices and avoiding random permutations, the framework not only simplifies algorithmic implementation but also significantly broadens the theoretical applicability of CSMC. This approach guarantees the validity of CSMC under substantially weaker conditions than previously required, thereby enhancing its robustness and flexibility in practical applications.

Abstract

Conditional sequential Monte Carlo (CSMC) algorithms arise in particle Markov chain Monte Carlo and a number of related settings. As in standard sequential Monte Carlo (SMC) algorithms, it is possible to employ a number of approaches to resampling within CSMC, but some additional care is required to arrive at a valid algorithm. We present a simple framework for implementing valid SMC and CSMC algorithms which (a) covers most known resampling schemes including those with a complicated dependence structure like systematic resampling, but also adaptive resampling, and even more `exotic' schemes like a version of chopthin resampling; (b) explains how to implement conditional analogues of these and other well known resampling schemes without randomly permuting/shifting the order of the ancestor indices; (c) requires only very weak assumptions which include neither (marginal) "unbiasedness" nor exchangeability.

Problem

• resampling
• conditional sequential Monte Carlo
• particle Markov chain Monte Carlo
• ancestor indices
• validity

Innovation

• conditional sequential Monte Carlo
• resampling
• particle Markov chain Monte Carlo
• systematic resampling
• chopthin