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Non-linear state space models are a widely-used class of models forbiological, economic, and physical processes. Fitting these models to observeddata is a difficult inference problem that has no straightforward solution. Wetake a Bayesian approach to the inference of unknown parameters of a non-linearstate model; this, in turn, requires the availability of efficient Markov ChainMonte Carlo (MCMC) sampling methods for the latent (hidden) variables and modelparameters. Using the ensemble technique of Neal (2010) and the embedded HMMtechnique of Neal (2003), we introduce a new Markov Chain Monte Carlo methodfor non-linear state space models. The key idea is to perform parameter updatesconditional on an enormously large ensemble of latent sequences, as opposed toa single sequence, as with existing methods. We look at the performance of thisensemble method when doing Bayesian inference in the Ricker model of populationdynamics. We show that for this problem, the ensemble method is vastly moreefficient than a simple Metropolis method, as well as 1.9 to 12.0 times moreefficient than a single-sequence embedded HMM method, when all methods aretuned appropriately. We also introduce a way of speeding up the ensemble methodby performing partial backward passes to discard poor proposals at lowcomputational cost, resulting in a final efficiency gain of 3.4 to 20.4 timesover the single-sequence method.

MCMC for non-linear state space models using ensembles of latent sequences