Sequential Monte Carlo methods: can we replace the resampling step?
Seminar Room 1, Newton Institute
Sequential Monte Carlo methods provide reliable approximations of the conditional ditribution of a certain signal process given the data obtined from an associated observation process. The generic SMC method involves sampling from the prior distribution of the signal and then using a weighted bootstrap technique (or equivalent) with weights defined by the likelihood of the most recent observation data. If the number of updating stages becomes large, the repeated application of the the weighted bootstrap may lead to what the literature describes as "impoverished sample" or "sample attrition". That means that the sample being carried forward will have fewer and fewer distict values. In this talk, I propose a method that attempts to solve this problem for the continuous time filtering problem. The method replaces the sampling from the prior step with sampling from a distribution that depends on the entire (existing) sample and the most recent observation data and it does not contain the weighted bootstrap step. The method is motivated by recent advances in the area of McKean-Vlasov representations for solutions of stochastic PDEs and their application to solving the filtering problem in a continuous time framework.