State-space models (SSM) constitute a natural framework for simultaneously describing the evolution of animal population abundances and the periodic observations made on the population. The components of a SSM are the state equations, that describe the evolution of animal abundance in time, and the observation equations. Often, these equations are non-linear, non-Gaussian and of high dimensionality. A typical feature of animal population modelling is that the state equations contain intermediate subprocesses (such as birth or migration) for which there are no observations (e.g. observations on the population may only be taken once a year). Usually, the objective is to conduct inference on various aspects of the state equations that capture features of interest about the population, on the basis of the observed data. We consider Bayesian inference.
The main objective of our work is the development of two types of algorithms for posterior computation, namely algorithms based on sequential Monte Carlo techniques as well as those based on Markov Chain Monte Carlo, and the subsequent comparison of their performances (from an applied, rather than theoretical, perspective). We will comment on some features that are important in order to increase the efficiency of the algorithms, and we will offer a comparison between both methodologies, with a view towards providing guidelines concerning computational approaches to fitting SSMs to wildlife animal populations.
We conclude with an application to a seals abundance dataset, where several colonies are considered and movement between colonies is also an issue.
This is joint work with Ken Newman, Steve Buckland and Len Thomas (University of St Andrews, UK)