Approximate bayesian computation for smoothing

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Title: Approximate bayesian computation for smoothing
Authors: Martin, JS
Jasra, A
Singh, SS
Whiteley, N
Del Moral, P
McCoy, E
Item Type: Journal Article
Abstract: We consider a method for approximate inference in hidden Markov models (HMMs). The method circumvents the need to evaluate conditional densities of observations given the hidden states. It may be considered an instance of Approximate Bayesian Computation (ABC) and it involves the introduction of auxiliary variables valued in the same space as the observations. The quality of the approximation may be controlled to arbitrary precision through a parameter ε > 0. We provide theoretical results which quantify, in terms of ε, the ABC error in approximation of expectations of additive functionals with respect to the smoothing distributions. Under regularity assumptions, this error is, where n is the number of time steps over which smoothing is performed. For numerical implementation, we adopt the forward-only sequential Monte Carlo (SMC) scheme of [14] and quantify the combined error from the ABC and SMC approximations. This forms some of the first quantitative results for ABC methods which jointly treat the ABC and simulation errors, with a finite number of data and simulated samples. © Taylor & Francis Group, LLC.
Issue Date: 4-May-2014
Date of Acceptance: 27-Dec-2013
URI: http://hdl.handle.net/10044/1/64619
DOI: https://dx.doi.org/10.1080/07362994.2013.879262
ISSN: 0736-2994
Publisher: Taylor & Francis
Start Page: 397
End Page: 420
Journal / Book Title: Stochastic Analysis and Applications
Volume: 32
Issue: 3
Copyright Statement: © 2014 Taylor & Francis. This is an Accepted Manuscript of an article published by Taylor & Francis in Stochastic Analysis and Applications on 04 May 2014, available online: https://dx.doi.org/10.1080/07362994.2013.879262
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/I019111/1
Keywords: stat.CO
stat.CO
stat.ME
0102 Applied Mathematics
0104 Statistics
1502 Banking, Finance And Investment
Statistics & Probability
Publication Status: Published
Online Publication Date: 2014-04-28
Appears in Collections:Mathematics
Statistics
Faculty of Natural Sciences



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