Advances in Applied Probability

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

M. N. M. van Lieshout and E. W. van Zwet

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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.

Article information

Source
Adv. in Appl. Probab. Volume 33, Number 2 (2001), 339-353.

Dates
First available in Project Euclid: 30 August 2001

Permanent link to this document
http://projecteuclid.org/euclid.aap/999188317

Digital Object Identifier
doi:10.1239/aap/999188317

Mathematical Reviews number (MathSciNet)
MR1842296

Zentralblatt MATH identifier
0982.62080

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 62M30: Spatial processes

Keywords
Boolean model coupling from the past Markov chain Monte Carlo simulation maximum likelihood estimation stochastic approximation EM algorithm stochastic EM algorithm

Citation

van Lieshout, M. N. M.; van Zwet, E. W. Exact sampling from conditional Boolean models with applications to maximum likelihood inference. Adv. in Appl. Probab. 33 (2001), no. 2, 339--353. doi:10.1239/aap/999188317. http://projecteuclid.org/euclid.aap/999188317.


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