Efficient methods for fitting nonlinear non-Gaussian state-space models of wildlife population dynamics

Recent years have seen an enormous growth in interest in and methods for fitting mechanistic
models of wildlife population dynamics to survey data on animal numbers, survival and birth rates.
Various statistical methods have been proposed, based both on maximum likelihood and Bayesian
approaches. Examples include the Kalman filter (and extensions) for maximum likelihood estimation
and Markov chain Monte Carlo (MCMC) or particle filtering for Bayesian models. Each has
advantages and disadvantages - for example the Kalman filter is designed for linear Gaussian models
(but seems to do remarkably well in other circumstances); MCMC is an excellent omnibus method
but it can be difficult to derive efficient samplers (i.e., those that produce reliable answers in a
reasonable amount of computer time); particle filtering is easy to program but very inefficient for
some models (e.g., those with random effects). In this project, we aim to blend aspects of these
approaches to increase the efficiency of the estimation. For example, we will investigate using
Kalman filter estimates as importance sampling starts in a particle filter algorithm, and using the
particle filter to provide proposals in an MCMC algorithm.