Resampling Strategy in Sequential Monte Carlo for Constrained Sampling Problems

Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different types of constraints. These constraints can make the problem much more challenging. In this paper, we formulate a general framework of using SMC for constrained sampling problems based on forward and backward pilot resampling strategies. We review some existing methods under the framework and develop several new algorithms. It is noted that all information observed or imposed on the underlying system can be viewed as constraints. Hence the approach outlined in this paper can be useful in many applications.