UNSPECIFIED (2003) A note on stochastic domination and conditional thinning. ADVANCES IN APPLIED PROBABILITY, 35 (4). pp. 937-940. ISSN 0001-8678

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Abstract

The motivation for this work came from the paper [7] by van Lieshout and van Zwet, where a simulation algorithm is proposed for obtaining samples from conditional Boolean models. This algorithm concerns a germ-grain random set model in which the germ process is homogeneous Poisson and grains are discs of fixed radius. The conditioning event to be considered was the coverage of an uncountable set; however, the algorithm was proposed for 'any conditioning event 9 such that, if a configuration x satisfies epsilon, then, for any x, x boolean OR {x} also satisfies epsilon' [7, p. 342]. We use this property to define the notion of an antihereditary conditioning event (Definition 1). The algorithm of van Lieshout and van Zwet was intended to be perfect (i.e. delivering an unbiased sample in finite time); unfortunately, it has been discovered that it is biased (see the correction note to [7]). This note summarizes the results in the technical report [4], where the bias of the algorithm of van Lieshout and van Zwet (which we call the VLVZ algorithm) is established and its nature explored using notions of stochastic domination.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	ADVANCES IN APPLIED PROBABILITY
Publisher:	APPLIED PROBABILITY TRUST
ISSN:	0001-8678
Date:	December 2003
Volume:	35
Number:	4
Number of Pages:	4
Page Range:	pp. 937-940
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/9101

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