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On the conditional distributions of spatial point processes

Part of:Inference from stochastic processesStochastic systems and controlGeometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

François Caron,
Pierre Del Moral,
Arnaud Doucet and
Michele Pace
François Caron*
Affiliation:
Université Bordeaux 1
Pierre Del Moral*
Affiliation:
Université Bordeaux 1
Arnaud Doucet*
Affiliation:
University of British Columbia
Michele Pace*
Affiliation:
Université Bordeaux 1
*
∗ Postal address: INRIA Sud-Ouest and Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cedex, France.
∗ Postal address: INRIA Sud-Ouest and Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cedex, France.
∗∗ Postal address: Department of Statistics, 333-6356 Agricultural Road, Vancouver BC, V6T 1Z2, Canada. Email address: arnaud@cs.ubc.ca
∗ Postal address: INRIA Sud-Ouest and Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cedex, France.
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Abstract

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We consider the problem of estimating a latent point process, given the realization of another point process. We establish an expression for the conditional distribution of a latent Poisson point process given the observation process when the transformation from the latent process to the observed process includes displacement, thinning, and augmentation with extra points. Our original analysis is based on an elementary and self-contained random measure theoretic approach. This simplifies and complements previous derivations given in Mahler (2003), and Singh, Vo, Baddeley and Zuyev (2009).

Keywords

Filteringmultitarget trackingspatial point processprobability hypothesis density filter

MSC classification

Primary:62M30: Spatial processes
Secondary:93E11: Filtering60D05: Geometric probability and stochastic geometry

Information

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 43 , Issue 2 , June 2011, pp. 301 - 307
Copyright
Copyright © Applied Probability Trust 2011 

References

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