SMC2, Sequential Inference in State-Space Models
Nicolas Chopin, Omiros Papaspiliopoulos · Springer series in statistics · 2020
SummaryIn Chap. 16, we discussed PMCMC algorithms, i.e., MCMC samplers that (a) rely on particle filters to approximate the intractable likelihood; yet (b) leave invariant the exact posterior distribution of the considered (state-space) model. Potentially, PMCMC algorithms suffer from the same limitations as all MCMC samplers: they do not offer an easy way to estimate marginal likelihoods; they are too expensive for sequential scenarios; and calibrating their tuning parameters may be cumbersome (recall the numerical experiments of Sect. 16.5.2).In Chap. 17, we discussed SMC samplers, which, among other benefits, address these shortcomings in situations where the likelihood may be computed exactly. The next logical step is to develop SMC samplers for models with intractable likelihoods.Such SMC samplers are often called SMC2, and are the subject of this chapter. The first part presents a basic, generic version of SMC2 algorithms. The second part develops a more elaborate variant, which makes it possible to perform simultaneously and sequentially parameter inference, model choice, and state prediction for state-space models.