SMC2: an efficient algorithm for sequential analysis of state space models

By Nicolas Chopin, Pierre E. Jacob, Omiros Papaspiliopoulos. 2011

386 citations recorded by the source corpus.

Summary. We consider the generic problem of performing sequential Bayesian inference in a state space model with observation process y, state process x and fixed parameter θ. An idealized approach would be to apply the iterated batch importance sampling algorithm of Chopin. This is a sequential Monte Carlo algorithm in the θ‐dimension, that samples values of θ, reweights iteratively these values by using the likelihood increments and rejuvenates the θ‐particles through a resampling step and a Markov chain Monte Carlo update step. In state space models these likelihood increments are intractable in most cases, but they may be unbiasedly estimated by a particle filter in the x‐dimension, for any fixed θ. This motivates the SMC2 algorithm that is proposed in the paper: a sequential Monte Carlo algorithm, defined in the θ‐dimension, which propagates and resamples many particle filters in the x‐dimension. The filters in the x‐dimension are an example of the random weight particle filter. In contrast, the particle Markov chain Monte Carlo framework that has been developed by Andrieu and colleagues allows us to design appropriate Markov chain Monte Carlo rejuvenation steps. Thus, the θ‐particles 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 non‐sequential applications and consider various degrees of freedom, as for example increasing dynamically the number of x‐particles. We contrast our approach with various competing methods, both conceptually and empirically through a detailed simulation study, and based on particularly challenging examples.

Subfields: Artificial Intelligence

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Citations in the corpus

Nested Sequential Monte Carlo Methods (2015, methodology): “The SMC2 by Chopin et al. (2013) and the recent method by Crisan & Mı́guez (2013) are sequential learning algorithms for state space models, where one SMC sampler for the parameters is coupled with another SMC sampler for the latent states.”
The correlated pseudomarginal method (2015, methodology): “Finally, a sequential extension of the particle marginal MH algorithm (Andrieu et al., 2010), a pseudomarginal method, has been proposed in Chopin et al. (2013) and it would be interesting to develop an efficient sequential version of the correlated pseudomarginal scheme.”
Bayesian State-Space Modelling on High-Performance Hardware Using LibBi (2013, methodology): “Variants of sequential Monte Carlo (SMC) [14] are particularly attractive, including particle Markov chain Monte Carlo (PMCMC) [4] and SMC2 [8].”
Importance Sampling Squared for Bayesian Inference in Latent Variable Models (2013, methodology): “Chopin et al. (2013) consider a sequential Monte Carlo procedure for sequential inference in space state models in which the intractable likelihood increments are estimated by sequential Monte Carlo, calling their method SMC2.”
Bayesian computation: a perspective on the current state, and sampling backwards and forwards (2015, background): “An extension to approximating the sequential ﬁltering distribution is found in Chopin et al. (2013).”
On Particle Methods for Parameter Estimation in State-Space Models (2014, methodology): “4 The SMC2 algorithm The SMC2 algorithm introduced simultaneously in [19] and [43] may be considered as the particle equivalent of Particle MCMC.”
Sequential Monte Carlo with Highly Informative Observations (2014, methodology): “It could be coupled with MCMC (as in particle MCMC, Andrieu, Doucet, and Holenstein [1]) or another level of SMC (as in SMC2, Chopin, Jacob, and Papaspiliopoulos [9]) for parameter estimation, however.”
Bayesian computation: a summary of the current state, and samples backwards and forwards (2015, background): “An extension to approximating the sequential ﬁltering distribution is found in Chopin et al. (2013).”