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

By Gareth William Peters, Geoffrey R. Hosack, Keith R. Hayes. 2010

47 citations recorded by the source corpus.

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 real and also synthetically generated data sets we examine the extent to which observation noise and process error may frustrate efforts to choose between these models. 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 Cram\'er-Rao Lower Bound of Tichavsk\'y (1998). We derive expressions for these Cram\'er-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 posterior 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.

Subfields: Demography, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/773c740e446b94a796451e16ffbd0f23ce9b65d7

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Citations in the corpus

Biips: Software for Bayesian Inference with Interacting Particle Systems (2014, background): “…economics and macro-economics (Pitt and Shephard 1999; Fernández-Villaverde and Rubio-Ramírez 2007; Flury and Shephard 2011; Del Moral et al. 2012), epidemiology (Cauchemez et al. 2008; Dureau et al. 2013), ecology (Buckland et al. 2007; Peters et al. 2010) or pharmacology (Donnet and Samson 2011).”
Towards Automatic Model Comparison: An Adaptive Sequential Monte Carlo Approach (2013, methodology): “Sophisticated variants of these algorithms, such as those developed in Peters et al. (2010), have been considered in recent years but depend upon essentially the same construction and ultimately require adequate mixing of the underlying Markov process.”
SMC2: an efficient algorithm for sequential analysis of state space models (2011, methodology): “Nevertheless, it calibrates automatically its tuning parameters, as for example Nx and the proposal distributions for θ. (Note that adaptive versions of PMCMC sampling (see for example Silva et al. (2009) and Peters et al. (2010)) exist, however.)”