SREL Reprint #0855

 

 

 

Characterizations of the Multivariate Ornstein-Uhlenbeck Diffusion Process in the Context of Home Range Analyses

James E. Dunn and I. Lehr Brisbin, Jr.

 

Abstract

This paper is a sequel to earlier work reported by the first author in which the MOU diffusion process was introduced as a model for radio telemetry studies in order to account for lack of independence of successive observations along the sample path.  The effects of perfectly reflecting physical boundaries on the model are considered.  To answer previous criticisms, it is demonstrated that a broad class of non-linear transformations can be used to map virtually any shape of home range into the elliptical form assumed by the model.  A formula for estimating the original area is given.  A MLE is proposed for data sampled at unequally spaced points in time.  Evaluation of matrix transcedental functions are considered in this context.  A method of characterizing the rate of travel intrinsic to the MOU process is given.  The success of a previously proposed test for dynamic territorial interaction is illustrated.  A simulation study indicates that the Type I error rate for this test is about twice the assumed value.

 

SREL Reprint #0855

Dunn, J.E. and I.L. Brisbin Jr. 1985. Characterizations of the multivariate Ornstein Uhlenbeck diffusion process in the context of home range analysis. In Statistical Theory and Data Analysis, edited by K. Matusita. p. 181-205. Elsevier Science Publications.

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