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

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

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

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

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.

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Related Works:

See: Correction. Adv. Appl. Prob. Vol. 35, No. 2 (2003), p. 362.

Project Euclid: euclid.aap/1051201651

Primary Subjects: 60D05, 62M30

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

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Links and Identifiers

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

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