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

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 part...

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Veröffentlicht in:Probability theory and related fields 2013-04, Vol.155 (3-4), p.665-701
Hauptverfasser: Eberle, Andreas, Marinelli, Carlo
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Marinelli, Carlo
description 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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source Springer Journals; Business Source Complete
subjects Approximation
Chain mobility
Constants
Dynamical systems
Dynamics
Economics
Evolution
Finance
Importance sampling
Insurance
Management
Markov analysis
Markov chains
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Monte Carlo methods
Monte Carlo simulation
Operations Research/Decision Theory
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Regularity
Resampling
Statistics for Business
System dynamics
Theoretical
title Quantitative approximations of evolving probability measures and sequential Markov chain Monte Carlo methods
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