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What is it?
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This is a Matlab package to estimate numerically:
- probabilities of rare events given by Prob(f(X) > q) where the distribution of X is known.
- quantiles related to rare event: q s.t. Prob(f(X) > q) = P
We provide two core processes labelled Estimator_A and Estimator_B.
The main advantage of Estimator_B is that its properties are proven whatever the size the particle set.
References about Estimator_A
- description of the algorithm and experimental assessment
Frederic Cerou, Teddy Furon, and Arnaud Guyader, "Experimental Assessment of the Reliability for Watermarking and Fingerprinting Schemes," EURASIP Journal on Information Security, vol. 2008, Article ID 414962, 12 pages, 2008. doi:10.1155/2008/414962
http://www.hindawi.com/journals/is/2008/414962/
- Its asymptotical properties
F. Cerou, P. Del Moral, T. Furon et A. Guyader. "Sequential Monte Carlo for Rare Event Estimation," Statistics and Computing, Accepted, 2011.
http://www.sites.univ-rennes2.fr/laboratoire-statistique/AGUYADER/doc/cdfg.pdf
References about Estimator_B
- description of the algorithm and its properties
A. Guyader, N. Hengartner et E. Matzner-Lober. Simulation and Estimation of Extreme Quantiles and Extreme Probabilities.
Applied Mathematics & Optimization, Accepted, 2011.
http://www.sites.univ-rennes2.fr/laboratoire-statistique/AGUYADER/doc/ghm.pdf
Prerequisites
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We have tested the software with relatively recent versions (R2010b, R2010a).
Octave users will probably have to squeeze the parser.
To run estimations, we need 3 functions:
- Objective function or scoring function f(.),
- Generator of occurences of X according to a given distribution P_X
- Modification function which modifies X into Y s.t. Y is still distributed as P_X
and lies in a controlled vicinity of X
Installation
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Nothing special. Include the toolbox directory with addpath.
There are test programs in the ./Tests directory.
Outputs are given in the ./Tests/html
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