Quantitative approximations of evolving probability measures and sequential Markov Chain Monte Carlo methods

Details Quantitative approximations of evolving probability measures and sequential Markov Chain Monte Carlo methods Quantitative approximations of evolving probability measures and sequential Markov Chain Monte Carlo methods

2010-10-08

arxiv.org/abs/1010.1696v2

Mathematics

Probability

28 pages, final version

Scientific paper

We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity conditions, we derive non-asymptotic error bounds for the particle system approximation. In a few simple examples, including high dimensional product measures, bounds with explicit constants of feasible size are obtained. Our main motivation are applications to sequential MCMC methods for Monte Carlo integral estimation.

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