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SURVEY OF CLASSICAL AND BAYESIAN APPROACHES TO THE CHANGE-POINT PROBLEM: FIXED SAMPLE AND SEQUENTIAL PROCEDURES OF TESTING AND ESTIMATION11Research supported in part by ONR Contracts N00014-75-0725 at The George Washington University and N00014-81-K-0407 at SUNY-Binghamton.
In ecology, if the considered area or space is large, the spatial distribution of individuals of a given plant species is never homogeneous; plants form different patches. The homogeneity change in space or in time (in particular, the related change-point problem) is an important research subject in mathematical statistics. In the paper, for a given data system along a straight line, two areas are considered, where the data of each area come from different discrete distributions, with unknown parameters. In the paper a method is presented for the estimation of the distribution change-point between both areas and an estimate is given for the distributions separated by the obtained change-point. The solution of this problem will be based on the maximum likelihood method. Furthermore, based on an adaptation of the well-known bootstrap resampling, a method for the estimation of the so-called change-interval is also given. The latter approach is very general, since it not only applies in the case of the maximum-likelihood estimation of the change-point, but it can be also used starting from any other change-point estimation known in the ecological literature. The proposed model is validated against typical ecological situations, providing at the same time a verification of the applied algorithms.
Acta Biotheoretica – Springer Journals
Published: Nov 6, 2009
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