統計数学セミナー
Seminar on Probability and Statistics |
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Seminar on Probability and Statistics Wednesday April 22 2009 Tokyo 128 3:00-4:10 pm
Interacting Markov chain Monte Carlo Methods for Solving Nonlinear Measure-Valued Equations
Arnaud DOUCET 統計数理研究所 / The Institute of Statistical Mathematics Abstract We present a new class of interacting Markov chain Monte Carlo
algorithms for solving numerically discrete-time measure-valued
equations. The associated stochastic processes belong to the class of
self-interacting Markov chains. In contrast to traditional Markov
chains, their time evolution depend on the occupation measure of their
past values. This general methodology allows us to provide a natural way
to sample from a sequence of target probability measures of increasing
complexity. We develop an original theoretical analysis to analyze the
behaviour of these iterative algorithms. We establish a variety of
convergence results including exponential estimates and a uniform
convergence theorem with respect to the number of target distributions.
We also illustrate these algorithms in the context of Feynman-Kac
distribution flows.
(this is joint work with Professor Pierre Del Moral) |
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