Nested Sequential Monte Carlo Methods

TL;DR

Nested Sequential Monte Carlo (NSMC) introduces a flexible framework for sampling from high-dimensional probability sequences by nesting approximate sampling procedures, enabling efficient inference in complex models.

Contribution

NSMC generalizes the SMC framework to allow nested, approximate, properly weighted samples, facilitating high-dimensional inference with arbitrary nesting levels.

Findings

Effective on filtering problems with 100-1000 dimensions

Allows constructing high-dimensional proposals via nesting

Demonstrates practical efficacy in complex models

Abstract

We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correct SMC algorithm. Furthermore, NSMC can in itself be used to produce such properly weighted samples. Consequently, one NSMC sampler can be used to construct an efficient high-dimensional proposal distribution for another NSMC sampler, and this nesting of the algorithm can be done to an arbitrary degree. This allows us to consider complex and high-dimensional models using SMC. We show results that motivate the efficacy of our approach on several filtering problems with dimensions in the order of 100 to 1 000.