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Title: Approximate Bayesian Computation for Smoothing
Authors: Martin, J.S.
Jasra, A. 
Singh, S.S.
Whiteley, N.
Del Moral, P.
McCoy, E.
Keywords: Approximate Bayesian Computation
Hidden Markov models
Sequential Monte Carlo
Issue Date: 2014
Citation: Martin, J.S., Jasra, A., Singh, S.S., Whiteley, N., Del Moral, P., McCoy, E. (2014). Approximate Bayesian Computation for Smoothing. Stochastic Analysis and Applications 32 (3) : 397-420. ScholarBank@NUS Repository.
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.
Source Title: Stochastic Analysis and Applications
ISSN: 15329356
DOI: 10.1080/07362994.2013.879262
Appears in Collections:Staff Publications

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