A pseudo-marginal sequential Monte Carlo online smoothing algorithm

We consider online computation of expectations additive state functionals under general path probability measures proportional to products unnormalised transition densities. These densities are assumed be intractable but possible estimate, with or without bias. Using pseudo-marginalisation techniques we able extend the particle-based, rapid incremental smoother (PaRIS) algorithm proposed in [Bernoulli 23(3) (2017) 1951–1996] this setting. The resulting algorithm, which has a linear complexity number particles and constant memory requirements, applies wide range challenging path-space Monte Carlo problems, including smoothing partially observed diffusion processes models likelihood. is furnished several theoretical results, central limit theorem, establishing its convergence numerical stability. Moreover, strong mixing assumptions establish novel O(nε) bound on asymptotic bias where n length ε controls transition-density estimators.