Resampling Strategy in Sequential Monte Carlo for Constrained Sampling Problems

Chencheng Cai, Rong Chen, Ming Lin

Abstract:

Monte Carlo sample paths of a dynamic system are useful for studying the underlying system
and making statistical inferences related to the system. In many applications, the dynamic system
being studied requires various types of constraints or observable features. In this study, we use a
sequential Monte Carlo framework to investigate efficient methods for generating sample paths (with
importance weights) from dynamic systems with rare and strong constraints. Specifically, we present
a general formulation of the constrained sampling problem. Under such a formulation, we propose a
flexible resampling strategy based on a potentially time-varying lookahead timescale, and identify the
corresponding optimal resampling priority scores based on an ensemble of forward or backward pilots.
Several examples illustrate the performance of the proposed methods.