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Sequential
Monte Carlo (SMC) methods are a set of flexible simulation-based
methods for sampling from a sequence of probability distributions; each
distribution being only known up to a normalising constant. These
methods were originally introduced in the early 50's by physicists and
have become very popular over the past few years in statistics and
related fields. For example, they are now extensively used to solve
sequential Bayesian inference problems arising in econometrics,
advanced signal processing or robotics.
SMC methods
approximate the sequence of probability distributions of interest using
a large set of random samples, named particles. These particles are
propagated over time using simple Importance Sampling (IS) and
resampling mechanisms. Asymptotically, i.e. as the number of particles
goes to infinity, the convergence of these particle approximations
towards the sequence of probability distributions can be ensured under
very weak assumptions. However, for practical implementations, a finite
and sometimes quite restricted number of particles has to be
considered. Much research is therefore devoted to the design of
efficient sampling strategies in order to sample particles in regions
of high probability mass.
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