Iterative Monte Carlo for extreme quantiles and extreme probabilities

22 mins 37 secs, 83.70 MB, iPod Video 480x360, 25.0 fps, 44100 Hz, 505.28 kbits/sec

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Description:	Guyader, A; Hengartner, NW; Matzner-Løber, E (Rennes 2; Los Alamos; Rennes 2) Monday 21 June 2010, 14:50-15:15

Created:

2010-06-25 08:25

Collection:

Stochastic Processes in Communication Sciences

Publisher:

Isaac Newton Institute

Matzner-Løber, E

Language:

eng (English)

Credits:

Author:

Matzner-Løber, E


Abstract:	Let $X$ be a random vector with distribution $\mu$ on ${\mathbb R}^d$ and $\Phi$ be a mapping from ${\mathbb R}^d$ to ${\mathbb R}$. That mapping acts as a black box, e.g., the result from some computer experiments for which no analytical expression is available. This paper presents an efficient algorithm to estimate a tail probability given a quantile or a quantile given a tail probability. It proceeds by successive elementary steps, each one being based on Metropolis-Hastings algorithm. The algorithm improves upon existing multilevel splitting methods and can be analyzed using Poisson process tools that lead to exact description of the distribution of the estimated probabilities and quantiles. The performance of the algorithm is demonstrated in a problem related to digital watermarking.

Abstract:

Let $X$ be a random vector with distribution $\mu$ on ${\mathbb R}^d$ and $\Phi$ be a mapping from ${\mathbb R}^d$ to ${\mathbb R}$. That mapping acts as a black box, e.g., the result from some computer experiments for which no analytical expression is available. This paper presents an efficient algorithm to estimate a tail probability given a quantile or a quantile given a tail probability. It proceeds by successive elementary steps, each one being based on Metropolis-Hastings algorithm. The algorithm improves upon existing multilevel splitting methods and can be analyzed using Poisson process tools that lead to exact description of the distribution of the estimated probabilities and quantiles. The performance of the algorithm is demonstrated in a problem related to digital watermarking.

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