Document: PER-3-91-3

Fitting population models with process noise and observation error.

DE VALPINE, P.* and A.HASTINGS

University of California, Davis, CA 95616 USA ¹

Abstract:
The problem of fitting population models to data is confounded by the combined effects of environmental variability and inaccurate observations. We evaluate a method that incorporates both process noise and observation error to fit models to time series data in a likelihood framework. The method numerically calculates likelihoods in a state-space formulation for nonlinear, non-Gaussian models that are analagous to the linear, Guassian likelihoods of the Kalman filter. We compare the method to two common methods, least squares with process noise only or with observation error only, using Beverton-Holt and Ricker models. The numerical state-space method had lower estimator bias and variance than the other methods in nearly all cases. The only exceptions were for the Ricker model with stable-point parameters and one of the noise variances small, i.e. close to least squares assumptions, in which case one of the least squares methods was superior. We also evaluated each method for model selection using information criteria. All methods were biased toward selecting the Ricker over the Beverton-Holt, even when data were generated with the Beverton-Holt. Least squares with process error was least biased for model selection. Convergence of likelihood ratios to theoretical asymptotic distributions was good for stable-point Ricker parameters, less accurate for two-cycle and four-cycle Ricker parameters, and least accurate for the Beverton-Holt model. The numerical state-space method offers a useful tool for connecting models and data and ecology.

Keywords: model fitting; Kalman filter

This abstract is being presented at: 3:15 PM in session:
Oral Session #46: Modeling Populations and Statistical Ecology.