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Simulating events of unknown probabilities via reverse time martingales

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Łatuszyński, Krzysztof, Kosmidis, Ioannis, Papaspiliopoulos, Omiros and Roberts, Gareth O. (2011) Simulating events of unknown probabilities via reverse time martingales. Random Structures & Algorithms, 38 (4). pp. 441-452. doi:10.1002/rsa.20333 ISSN 1042-9832.

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Official URL: http://dx.doi.org/10.1002/rsa.20333

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Abstract

Let s is an element of (0, 1) be uniquely determined but only its approximations can be obtained with a finite computational effort. Assume one aims to simulate an event of probability s. Such settings are often encountered in statistical simulations. We consider two specific examples. First, the exact simulation of non-linear diffusions ([3]). Second, the celebrated Bernoulli factory problem ([10, 13]) of generating an f (p)-coin given a sequence X(1), X(2), ... of independent tosses of a p-coin (with known f and unknown p). We describe a general framework and provide algorithms where this kind of problems can be fitted and solved. The algorithms are straightforward to implement and thus allow for effective simulation of desired events of probability s. Our methodology links the simulation problem to existence and construction of unbiased estimators.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH): Martingales (Mathematics), Probabilities
Journal or Publication Title: Random Structures & Algorithms
Publisher: John Wiley & Sons, Inc.
ISSN: 1042-9832
Official Date: June 2011
Dates:
DateEvent
June 2011Published
25 May 2010Available
10 November 2009Accepted
Volume: 38
Number: 4
Page Range: pp. 441-452
DOI: 10.1002/rsa.20333
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 16 February 2018
Date of first compliant Open Access: 16 February 2018
Funder: Engineering and Physical Sciences Research Council (EPSRC), Spain
Grant number: EP/G026521/1 and EP/D002060/1 (EPSRC), MTM2008-06660 (Spain)
Version or Related Resource: Łatuszyński, K., et al. (2009). Simulating events of unknown probabilities via reverse time martingales. [Coventry] : University of Warwick. Centre for Research in Statistical Methodology. (Working papers, no.09-30). http://wrap.warwick.ac.uk/id/eprint/35218
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