A Sharp First Order Analysis of Feynman-Kac Particle Models
JASRA, Ajay
Department of Computing [London]
Department of Statistics and Applied Probability [DSAP]
Department of Computing [London]
Department of Statistics and Applied Probability [DSAP]
JASRA, Ajay
Department of Computing [London]
Department of Statistics and Applied Probability [DSAP]
< Reduce
Department of Computing [London]
Department of Statistics and Applied Probability [DSAP]
Language
en
Rapport
This item was published in
2014-11-14
English Abstract
This article provides a new theory for the analysis of forward and backward particle approximations of Feynman-Kac models. Such formulae are found in a wide variety of applications and their numerical (particle) approximation ...Read more >
This article provides a new theory for the analysis of forward and backward particle approximations of Feynman-Kac models. Such formulae are found in a wide variety of applications and their numerical (particle) approximation are required due to their intractability. Under mild assumptions, we provide sharp and non-asymptotic first order expansions of these particle methods, potentially on path space and for possibly unbounded functions. These expansions allows one to consider upper and lower bound bias type estimates for a given time horizon n and particle number N ; these non-asymptotic estimates are of order O(n/N). Our approach is extended to tensor products of particle density profiles, leading to new sharp and non-asymptotic propagation of chaos estimates. The resulting upper and lower bound propagation of chaos estimates seems to be the first result of this kind for mean field particle models. As a by-product of our results, we also provide some analysis of the particle Gibbs sampler, providing first order expansions of the kernel and minorization estimates.Read less <
English Keywords
Feynman-Kac Formulae
Particle Simulation
Particle Gibbs Samplers
Origin
Hal imported