In this article, we present an overview of methods for sequential simulation from posterior distributions.
These methods are of particular interest in Bayesian filtering for discrete time dynamic models
that are typically nonlinear and non-Gaussian. A general importance sampling framework is developed
that unifies many of the methods which have been proposed over the last few decades in several
different scientific disciplines. Novel extensions to the existing methods are also proposed.We showin
particular how to incorporate local linearisation methods similar to those which have previously been
employed in the deterministic filtering literature these lead to very effective importance distributions.
Furthermore we describe a method which uses Rao-Blackwellisation in order to take advantage of
the analytic structure present in some important classes of state-space models. In a final section we
develop algorithms for prediction, smoothing and evaluation of the likelihood in dynamic models.
Hybrid Monte Carlo sampling.SAMPLES = HMC(F, X, OPTIONS, GRADF) uses a hybrid Monte Carlo
algorithm to sample from the distribution P ~ EXP(-F), where F is the
first argument to HMC. The Markov chain starts at the point X, and
the function GRADF is the gradient of the `energy function F.
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