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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
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Official URL: http://dx.doi.org/10.1002/rsa.20333
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 | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of 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: |
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| 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 | ||||||||
| 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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