Bayesian parameter estimation in dynamic population model via particle Markov chain Monte Carlo

Abstract

In nature, population dynamics are subject to multiple sources of stochasticity. State-space models (SSMs) provide an ideal framework for incorporating both environmental noises and measurement errors into dynamic population models. In this paper, we present a recently developed method, Particle Markov Chain Monte Carlo (Particle MCMC), for parameter estimation in nonlinear SSMs. We use one effective algorithm of Particle MCMC, Particle Gibbs sampling algorithm, to estimate the parameters of a state-space model of population dynamics. The posterior distributions of parameters are derived given the conjugate prior distribution. Numerical simulations showed that the model parameters can be accurately estimated, no matter the deterministic model is stable, periodic or chaotic. Moreover, we fit the model to 16 representative time series from Global Population Dynamics Database (GPDD). It is verified that the results of parameter and state estimation using Particle Gibbs sampling algorithm are satisfactory for a majority of time series. For other time series, the quality of parameter estimation can also be improved, if prior knowledge is constrained. In conclusion, Particle Gibbs sampling algorithm provides a new Bayesian parameter inference method for studying population dynamics.

Keywords

• Ricker model
• state-space model
• time series
• Bayesian inference
• particle Gibbs sampling