Document: LEL-3-20-2

Composite likelihood based inference for measurement error problems in population dynamics.

LELE, S.*

Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada. ¹

Abstract:
Conservation biologists and ecological scientists depend heavily on the population dynamics models for making conservation decisions and for understanding the underlying ecological mechanisms. Relating these models to the observed time or space-time series data from various biological surveys is a challenging statistical problem. There are two factors that make statistical inference challenging: 1) Even without any measurement error, standard likelihood based approaches are analytically difficult, 2) Incorporation of the measurement error increases the analytical and computational difficulty exponentially. In this paper, I suggest a method of inference based on the concepts of composite likelihood and estimating functions. Instead of trying to write the composite likelihood in an analytical fashion (which may not even be possible for realistic models), we use monte-carlo methods to estimate it. This 'simulated composite likelihood' function, when maximized, yields consistent and asymptotically normal estimators. Moreover, the computational burden of this method, although intensive, is not excessive. I will discuss the general ideas behind this method and then present results for Ricker (Logistic) model with Poisson measurement error. I will illustrate the method using a portion of the Breeding Bird Survey data, thus showing its practical feasibility and applicability.

Keywords: Hierarchical models, Observer error, Logistic growth, Poisson errors

This abstract is being presented at: 9:00 AM in session:
Symposium # 15: Measurement Error in Ecological Data.