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Simulating events of unknown probabilities via reverse time martingales
Author(s) -
Łatuszyński Krzysztof,
Kosmidis Ioannis,
Papaspiliopoulos Omiros,
Roberts Gareth O.
Publication year - 2011
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20333
Subject(s) - sequence (biology) , bernoulli's principle , event (particle physics) , estimator , algorithm , computer science , mathematics , mathematical optimization , discrete mathematics , statistics , engineering , genetics , physics , quantum mechanics , biology , aerospace engineering
Let s ∈(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. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 38, 441–452, 2011