Workshop on Statistical Methods for Dynamic
Vancouver, June 4-6 2009
System Models
Ecological population dynamics often involve high stochasticity, high sampling variance, and limited knowledge of biological details beyond the demographic constraints of stage- and age-structured development. I will summarize progress on maximum likelihood estimation and related inference for state-space models of population dynamics. State-space models include a stochastic model for dynamics of the true (unknown) population state and a stochastic observation model relating data and true states. For low-dimensional states, grid-based integration can be used, a numerical generalization of the Kalman Filter. For high-dimensional states such as ages and stages, Monte Carlo methods can be made to work, but an example will be given where approaches such as Monte Carlo Expectation Maximization, Particle Filtering, or direct Monte Carlo integration were very inefficient. A new method was developed based on weighted kernel smoothing of a Bayesian posterior. Simulations illustrate that, using two accuracy improvements, one can obtain good mode (maximum likelihood) location estimates even in up to 20 parameter dimensions, i.e. many more dimensions than good kernel estimates of the entire surface can be expected for. For the next step of an analysis problem -- obtaining the missing normalizing constant needed for likelihood ratio tests, model selection, and the like -- I give improvements to the bridge-sampling approach that can decrease error by an order of magnitude in some cases. The approaches will be illustrated with examples from fish and insect data.
Estimating biologically realistic models for noisy, nonlinear population dynamics structured by age and development stage
Assistant Professor
Environmental Science, Policy and Management
University of California, Berkeley
Berkeley, California
