SREL Reprint #0855
 

Characterizations of the Multivariate OrnsteinUhlenbeck
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 nonlinear 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. 181205. Elsevier Science
Publications.
