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Simulating Events of Unknown Probabilities via
Reverse Time Martingales.
Krzystof \L atuszy\'nski, K., Ioannis Kosmidis, Omiros Papaspiliopoulos and Gareth Roberts
Random Structures and Algorithms
2009.
AbstractLet $s\in
(0,1)$ 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
(\cite{BeskosRobertsEA1}). Second,
the celebrated Bernoulli factory problem (\cite{KeaneOBrien},
\cite{NacuPeres}) 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. [Edit]
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