Efficient SMC2 schemes for stochastic kinetic models

Golightly, Andrew and Kypraios, Theodore (2017) Efficient SMC2 schemes for stochastic kinetic models. Statistics and Computing . ISSN 1573-1375

[img]
Preview
PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Available under Licence Creative Commons Attribution.
Download (700kB) | Preview

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.

Item Type: Article
Keywords: Auxiliary particle filter (APF); Bayesian inference; Markov jump process (MJP); Sequential Monte Carlo (SMC); Stochastic kinetic model (SKM)
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1007/s11222-017-9789-8
Depositing User: Eprints, Support
Date Deposited: 28 Nov 2017 12:58
Last Modified: 29 Nov 2017 06:56
URI: http://eprints.nottingham.ac.uk/id/eprint/48416

Actions (Archive Staff Only)

Edit View Edit View