Titlebook: An Introduction to Sequential Monte Carlo; Nicolas Chopin,Omiros Papaspiliopoulos Textbook 2020 Springer Nature Switzerland AG 2020 Partic

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Introduction to State-Space Models,ine informally state-space models, and discuss several typical examples of such models from different areas of Science..However, we warn readers beforehand that we will need the mathematical machinery developed in the following chapters to define in sufficient generality state-space models, to devel

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Beyond State-Space Models,SMC may be used in other contexts. Notably, it may be applied to any computational task that may formulated as an artificial filtering problem. We briefly review in this chapter some of these extra applications of SMC and their connection to state-space models. In particular, we discuss rare-event s

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Finite State-Spaces and Hidden Markov Models,d backward recursions become sums over . terms, which can be computed exactly at a cost that is shown to be .. State-space models with a finite state-space model are usually called hidden Markov models. Applying the generic algorithm to their “bootstrap” Feynman-Kac formalisation yields an exact alg

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Linear-Gaussian State-Space Models,l is linear and Gaussian. The corresponding algorithms are commonly known as the Kalman filter and the Kalman smoother. The recursions follow immediately from the generic formulae of Chap. ., but in this setting they become linear algebra calculations. Various alternative, mathematically equivalentl

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Importance Sampling,ering (or related) distributions. This chapter covers the basics of importance sampling; resampling will be treated in the following chapter. We describe in particular the two versions of importance sampling (normalised and auto-normalised), we make a connection with the probabilistic notion of chan

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Importance Resampling, importance sampling technique. However it deserves a separate chapter because it plays a central role in particle filtering. In particular, we explain that resampling has the curious property of potentially reducing the variance at a later stage, provided that this later stage corresponds to a Mark