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Martin JS, Jasra A, Singh SS, et al., 2014, Approximate Bayesian computation for smoothing, Stochastic Analysis and Applications, Vol: 32, Pages: 397-420, ISSN: 0736-2994
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.
Martin JS, Jasra A, McCoy E, 2013, Inference for a class of partially observed point process models, Annals of the Institute of Statistical Mathematics, Vol: 65, Pages: 413-437, ISSN: 0020-3157
This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon sequential Monte Carlo methods, investigating the problems of performing sequential filtering and smoothing in complex examples, where current methods often fail. We consider various approaches for approximating posterior distributions using SMC. Our approaches, with some theoretical discussion are illustrated on a doubly stochastic point process applied in the context of finance.
Jasra A, Singh SS, Martin JS, et al., 2012, Filtering via approximate Bayesian computation, STATISTICS AND COMPUTING, Vol: 22, Pages: 1223-1237, ISSN: 0960-3174
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