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Exact sampling from conditional Boolean models with applications to maximum likelihood inference

Part of: Inference from stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

M. N. M. van Lieshout  and
E. W. van Zwet
M. N. M. van Lieshout*
Affiliation:
CWI
E. W. van Zwet*
Affiliation:
University of California, Berkeley
*
∗ Postal address: CWI, PO Box 94079, 1090 GB Amsterdam, The Netherlands. Email address: [email protected]
∗∗ Postal address: University of California, Department of Statistics, 367 Evans Hall # 3860, Berkeley, CA 94720-3860, USA.
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Abstract

We are interested in estimating the intensity parameter of a Boolean model of discs (the bombing model) from a single realization. To do so, we derive the conditional distribution of the points (germs) of the underlying Poisson process. We demonstrate how to apply coupling from the past to generate samples from this distribution, and use the samples thus obtained to approximate the maximum likelihood estimator of the intensity. We discuss and compare two methods: one based on a Monte Carlo approximation of the likelihood function, the other a stochastic version of the EM algorithm.

Keywords

Boolean modelcoupling from the pastMarkov chain Monte Carlo simulationmaximum likelihood estimationstochastic approximation EM algorithmstochastic EM algorithm

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 62M30: Spatial processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 33 , Issue 2 , June 2001 , pp. 339 - 353
Copyright
Copyright © Applied Probability Trust 2001 

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