SMC^2: an efficient algorithm for sequential analysis of statespace models
Chopin, Nicolas; Jacob, Pierre E.; Papaspiliopoulos, Omiros (2013), SMC^2: an efficient algorithm for sequential analysis of statespace models, Journal of the Royal Statistical Society. Series B, Statistical Methodology, 75, 3, p. 397426. http://dx.doi.org/10.1111/j.14679868.2012.01046.x
Type
Article accepté pour publication ou publiéDate
2013Journal name
Journal of the Royal Statistical Society. Series B, Statistical MethodologyVolume
75Number
3Publisher
Wiley
Pages
397426
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Show full item recordAbstract (EN)
We consider the generic problem of performing sequential Bayesian inference in a statespace model with observation process y, state process x and fixed parameter theta. An idealized approach would be to apply the iterated batch importance sampling (IBIS) algorithm of Chopin (2002). This is a sequential Monte Carlo algorithm in the thetadimension, that samples values of theta, reweights iteratively these values using the likelihood increments p(y_ty_1:t1, theta), and rejuvenates the thetaparticles through a resampling step and a MCMC update step. In statespace models these likelihood increments are intractable in most cases, but they may be unbiasedly estimated by a particle filter in the xdimension, for any fixed theta. This motivates the SMC^2 algorithm proposed in this article: a sequential Monte Carlo algorithm, defined in the thetadimension, which propagates and resamples many particle filters in the xdimension. The filters in the xdimension are an example of the random weight particle filter as in Fearnhead et al. (2010). On the other hand, the particle Markov chain Monte Carlo (PMCMC) framework developed in Andrieu et al. (2010) allows us to design appropriate MCMC rejuvenation steps. Thus, the thetaparticles target the correct posterior distribution at each iteration t, despite the intractability of the likelihood increments. We explore the applicability of our algorithm in both sequential and nonsequential applications and consider various degrees of freedom, as for example increasing dynamically the number of xparticles. We contrast our approach to various competing methods, both conceptually and empirically through a detailed simulation study, included here and in a supplement, and based on particularly challenging examples.Subjects / Keywords
Iterated batch importance sampling; Particle Markov chain Monte Carlo; Sequential Monte Carlo; Statespace models; Particle lteringRelated items
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