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Center for Nonlinear Studies |
Let X denote a generic random variable with probability distribution μ on Rd, and let Φ be a mapping from Rd to R. That mapping can be a black box, e.g., the result from some computer experiments for which no analytical expression is available. Our goal is to generate an i.i.d. sample (X1, . . . , XN ) with Xi ∼ L(X|Φ(X) > q) together with the probability P[Φ(X) > q] for any arbitrary real number q. When q lies far out in the right-hand tail of the distribution of the random variable Φ(X), a naive Monte-Carlo simulation becomes computationally intractable. In this article we present and analyse a novel simulation algorithm for this problem. It proceeds by successive elementary steps, each one being based on Metropolis-Hastings algorithm. Our technique is useful for both estimating the probability of events and estimating extreme quantiles. We demonstrate the practical usefulness of our method by applying it to a problem in watermarking.
Host: Humberto C Godinez Vazquez, Mathematical Modeling and Analysis Theoretical Division, 5-9188