UDC 519.218.5+519.246.5

IDENTIFICATION OF THE POINT PROCESS INTENSITY SHAPE

WITH THE PRECEDENTS MAXIMUM LIKELIHOOD DISTRIBUTIONS

 

V. E. Antsiperov

Kotelnikov Institute of Radioengineering and Electronics of the Russian Academy of Sciences, Mokhovaya 11-7, Moscow 125009, Russia

 

The paper is received on December 11, 2017

 

Abstract: The work is devoted to the point process intensity shape identification by a given realization of process point occurrences. This identification is supposed to be the best fitting of the registered point-set to formal description of intensity shapes of previously observed processes − precedents. As a formal description of intensity shapes, it is suggested to use the parameters of the probabilistic mixture models. The main argument in favor of such a description is the fact, that for Poisson point processes, conditional, at a given number of points, distribution of the single point occurrence coincides, with an accuracy up to normalization, with the intensity. Because the Poisson model has proven itself in many applied problems, potentially approach proposed has the large amount of applications. Moreover, since for the mixture-like approximations exist effective algorithms for mixture parameters computation, the numerical realization of the approach seems to be the most reliable in many respects. The mentioned algorithms belong to the well-known VM (VB EM) family, they implement iterative (recursive) realization of the maximum likelihood approach. We also present and discuss VM-like identification algorithms in our paper. In this connection, explicit expressions are given for the point process intensity shape iterative identification.

Key words:  point process intensity shape identification, formal shape description, inhomogeneous Poison point process, finite mixture models, machine learning, effective computational schemes, EM, VB EM, VM algorithms.

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For citation:

V. E. Antsiperov. Identification of the point process intensity shape with the precedents maximum likelihood distributions. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2017. No. 12. Available at http://jre.cplire.ru/jre/dec17/11/text.pdf.