Simulation and Estimation of Extreme Quantiles and Extreme Probabilities

Let X be a random vector with distribution μ on ℝ d and Φ be a mapping from ℝ d to 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 q...

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Bibliographic Details
Published in:Applied mathematics & optimization Vol. 64; no. 2; pp. 171 - 196
Main Authors: Guyader, Arnaud, Hengartner, Nicolas, Matzner-Løber, Eric
Format: Journal Article
Language:English
Published: New York Springer-Verlag 01.10.2011
Springer Nature B.V
Springer Verlag (Germany)
Subjects:
ALGORITHMS
Calculus of Variations and Optimal Control; Optimization
Computer simulation
COMPUTERIZED SIMULATION
Control
Digital broadcasting
Digital rights management
Digital watermarks
False alarms
Information technology
MAPPING
Mathematical analysis
Mathematical and Computational Physics
MATHEMATICAL METHODS AND COMPUTING
Mathematical Methods in Physics
Mathematical models
Mathematics
Mathematics and Statistics
Monte Carlo simulation
Numerical and Computational Physics
Optimization
Poisson distribution
PROBABILITY
Quantiles
RANDOMNESS
Simulation
Studies
Systems Theory
Theoretical
VECTORS
Vectors (mathematics)
Rare event
Metropolis-Hastings
Monte Carlo simulation
Watermarking
ISSN:0095-4616, 1432-0606
Online Access:Get full text
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Description
Summary:Let X be a random vector with distribution μ on ℝ d and Φ be a mapping from ℝ d to 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. 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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ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-011-9135-z