  Non-linear state space models are a widely-used class of models for
biological, economic, and physical processes. Fitting these models to observed
data is a difficult inference problem that has no straightforward solution. We
take a Bayesian approach to the inference of unknown parameters of a non-linear
state model; this, in turn, requires the availability of efficient Markov Chain
Monte Carlo (MCMC) sampling methods for the latent (hidden) variables and model
parameters. Using the ensemble technique of Neal (2010) and the embedded HMM
technique of Neal (2003), we introduce a new Markov Chain Monte Carlo method
for non-linear state space models. The key idea is to perform parameter updates
conditional on an enormously large ensemble of latent sequences, as opposed to
a single sequence, as with existing methods. We look at the performance of this
ensemble method when doing Bayesian inference in the Ricker model of population
dynamics. We show that for this problem, the ensemble method is vastly more
efficient than a simple Metropolis method, as well as 1.9 to 12.0 times more
efficient than a single-sequence embedded HMM method, when all methods are
tuned appropriately. We also introduce a way of speeding up the ensemble method
by performing partial backward passes to discard poor proposals at low
computational cost, resulting in a final efficiency gain of 3.4 to 20.4 times
over the single-sequence method.
