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

**Alexander Y. Shestopaloff
,
Dept. of Statistical Sciences, University of Toronto**

Radford M. Neal,
Dept. of Statistical Sciences and Dept. of Computer Science,
University of Toronto

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.

Technical report, 30 April 2013, 18 pages:
pdf.

Also available
from arXiv.org.