Advances in Applied Probability

On the conditional distributions of spatial point processes

François Caron, Pierre Del Moral, Arnaud Doucet, and Michele Pace

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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).

Article information

Adv. in Appl. Probab. Volume 43, Number 2 (2011), 301-307.

First available in Project Euclid: 21 June 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M30: Spatial processes
Secondary: 93E11: Filtering [See also 60G35] 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Filtering multitarget tracking spatial point process probability hypothesis density filter


Caron, François; Del Moral, Pierre; Doucet, Arnaud; Pace, Michele. On the conditional distributions of spatial point processes. Adv. in Appl. Probab. 43 (2011), no. 2, 301--307.

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