Ecological non-linear state space model selection via adaptive particle Markov chain Monte Carlo

Abstract:

We develop a novel advanced Particle Markov chain Monte Carlo algorithm that is capable of sampling from the posterior distribution of non-linear state space models for both the unobserved latent states and the unknown model parameters. We apply this novel methodology to five population growth models, including models with strong and weak Allee effects, and test if it can efficiently sample from the complex likelihood surface that is often associated with these models. Utilising synthetically generated data sets we examine the extent to which observation noise and process error may frustrate efforts to choose between these models in real ecological data sets. Our novel algorithm involves an Adaptive Metropolis proposal combined with an SIR Particle MCMC algorithm (AdPMCMC). We show that the AdPMCMC algorithm samples complex, high-dimensional spaces efficiently, and is therefore superior to standard Gibbs or Metropolis Hastings algorithms that are known to converge very slowly when applied to the non-linear state space ecological models considered in this paper. Additionally, we show how the AdPMCMC algorithm can be used to recursively estimate the Bayesian Cramer-Rao Lower Bound. We derive expressions for these Cramer-Rao Bounds and estimate them for the models considered. Our results demonstrate a number of important features of common population growth models, most notably their multi-modal likelihood surfaces and dependence between the static and dynamic parameters. We conclude by sampling from the posterior distribution of each of the models, and use Bayes factors to highlight how observation noise significantly diminishes our ability to select among some of the models, particularly those that are designed to reproduce an Allee effect. These results have important ramifications for ecologists searching for evidence of all forms of density dependence in population time series. This is a joint work with Gareth Peters (UNSW) and Keith Hayes (CSIRO).  

About the speaker: Dr Geoff Hosack is a researcher based at CSIRO Mathematics, Informatics and Statistics, in Hobart. His research aims at improving our understanding of ecosystem function while characterizing the uncertainty in model structure and parameters.