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Efficient SMC2 schemes for stochastic kinetic models

Golightly, Andrew; Kypraios, Theodore

Authors

Andrew Golightly

Theodore Kypraios theodore.kypraios@nottingham.ac.uk



Abstract

Fitting stochastic kinetic models represented by Markov jump processes within the Bayesian paradigm is complicated by the intractability of the observed-data likelihood. There has therefore been considerable attention given to the design of pseudo-marginal Markov chain Monte Carlo algorithms for such models. However, these methods are typically computationally intensive, often require careful tuning and must be restarted from scratch upon receipt of new observations. Sequential Monte Carlo (SMC) methods on the other hand aim to efficiently reuse posterior samples at each time point. Despite their appeal, applying SMC schemes in scenarios with both dynamic states and static parameters is made difficult by the problem of particle degeneracy. A principled approach for overcoming this problem is to move each parameter particle through a Metropolis-Hastings kernel that leaves the target invariant. This rejuvenation step is key to a recently proposed SMC2 algorithm, which can be seen as the pseudo-marginal analogue of an idealised scheme known as iterated batch importance sampling. Computing the parameter weights in SMC2 requires running a particle filter over dynamic states to unbiasedly estimate the intractable observed-data likelihood up to the current time point. In this paper, we propose to use an auxiliary particle filter inside the SMC2 scheme. Our method uses two recently proposed constructs for sampling conditioned jump processes, and we find that the resulting inference schemes typically require fewer state particles than when using a simple bootstrap filter. Using two applications, we compare the performance of the proposed approach with various competing methods, including two global MCMC schemes.

Journal Article Type Article
Journal Statistics and Computing
Print ISSN 0960-3174
Electronic ISSN 1573-1375
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
APA6 Citation Golightly, A., & Kypraios, T. (in press). Efficient SMC2 schemes for stochastic kinetic models. Statistics and Computing, https://doi.org/10.1007/s11222-017-9789-8
DOI https://doi.org/10.1007/s11222-017-9789-8
Keywords Auxiliary particle filter (APF); Bayesian inference; Markov jump process (MJP); Sequential Monte
Carlo (SMC); Stochastic kinetic model (SKM)
Publisher URL https://doi.org/10.1007/s11222-017-9789-8
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0





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