Fitting complex population models by combining particle filters with markov chain Monte Carlo

Background/Question/Methods

Markov chain Monte Carlo (MCMC) has become a standard tool for estimating state space models of population dynamics. Part of the reason behind its popularity is the availability of generic software such as WinBUGS and JAGS that allow fitting of complex population models without needing to program the details of the MCMC algorithms. While those programs are convenient and flexible tools they have their limitations. For instance, WinBUGS and JAGS only offer rudimentary model selection procedures and slow mixing may impede fitting of certain complex models.

An alternative technique for estimating the hidden states of state space models is provided by particle filters.  The most basic and generic particle filter is simple to implement for a wide range of complex models, including models for which MCMC can be problematic. Estimation of model parameters can be incorporated into particle filters, but this can be challenging. A recently developed alternative is to combine particle filters with MCMC by letting a particle filter explore the hidden states and using MCMC to estimate model parameters. These methods typically require only minimal analytical computations and are potentially applicable to a wide range population models. Furthermore they may provide estimates of marginal likelihoods for model comparisons.

Results/Conclusions

We illustrate how particle Metropolis Hastings methods may be used to fit population models by analyzing time series data on a red kangaroo (Macropus rufus) population in New South Wales, Australia. We fit three population models to these data, accounting for measurement error, using a particle Metropolis Hastings algorithm; a density dependent logistic diffusion model with environmental variance, an unregulated stochastic exponential growth model and a random walk model. Bayesian posterior model probabilities and Bayes-factors show that there is little support for density dependence and that the random walk model is the preferred model.

The particle Metropolis Hastings algorithm is a brute force method for fitting a range of complex population models. It is relatively simple to implement and to adapt between different models while it allows estimation of marginal densities for model selection. The cost is mainly computational which may result in long running times. However, the computational costs may partly be bypassed by parallelization.