Error Bounds and Normalizing Constants for Sequential Monte Carlo Samplers in High Dimensions

In this article we develop a collection of results associated to the analysis of the Sequential Monte Carlo (SMC) samplers algorithm, in the context of high-dimensional i.i.d. target probabilities. The SMC samplers algorithm can be designed to sample from a single probability distribution, using Monte Carlo to approximate expectations w.r.t. this law. Given a target density in d−dimensions our results are concerned with d → ∞, while the number of Monte Carlo samples, N , remains fixed. We deduce an explicit bound on the Monte-Carlo error for estimates derived using the SMC sampler and the exact asymptotic relative L2-error of the estimate of the normalizing constant associated to the target. We also establish marginal propagation of chaos properties of the algorithm. These results are deduced when the cost of the algorithm is O(Nd).