Variance estimation in adaptive sequential Monte Carlo

Sequential Monte Carlo (SMC) methods represent a classical set of techniques to simulate sequence probability measures through simple selection/mutation mechanism. However, the associated selection functions and mutation kernels usually depend on tuning parameters that are first importance for efficiency algorithm. A standard way address this problem is apply adaptive sequential (ASMC) methods, which consist in exploiting information given by history sample tune parameters. This article concerned with variance estimation such ASMC methods. Specifically, we focus case where asymptotic coincides one “limiting” algorithm as defined Beskos et al. (Ann. Appl. Probab. 26 (2016) 1111–1146). We prove that, under natural assumptions, estimator introduced Lee Whiteley (Biometrika 105 (2018) 609–625) nonadaptive (i.e., SMC) also consistent To do this, introduce new expressed terms coalescent tree-based measures, explain its connection previous one. Our constructed tracing genealogy interacting particle system. The tools use connect study Markov chain SMC As such, they may give some insights when dealing complex genealogy-involved problems systems more general scenarios.