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 exible 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.

Key words and phrases: Constrained sampling, pilot, priority score, resampling, sequential Monte Carlo.