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Journal Articles ESAIM: Proceedings Year : 2015

Hastings-Metropolis algorithm on Markov chains for small-probability estimation

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Abstract

Shielding studies in neutron transport, with Monte Carlo codes, yield challenging problems of small-probability estimation. The particularity of these studies is that the small probability to estimate is formulated in terms of the distribution of a Markov chain, instead of that of a random vector in more classical cases. Thus, it is not straightforward to adapt classical statistical methods, for estimating small probabilities involving random vectors, to these neutron-transport problems. A recent interacting-particle method for small-probability estimation, relying on the Hastings-Metropolis algorithm, is presented. It is shown how to adapt the Hastings-Metropolis algorithm when dealing with Markov chains. A convergence result is also shown. Then, the practical implementation of the resulting method for small-probability estimation is treated in details, for a Monte Carlo shielding study. Finally, it is shown, for this study, that the proposed interacting-particle method considerably outperforms a simple Monte Carlo method, when the probability to estimate is small.
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Dates and versions

hal-01058939 , version 1 (08-09-2014)
hal-01058939 , version 2 (20-11-2014)
hal-01058939 , version 3 (27-11-2014)
hal-01058939 , version 4 (28-11-2014)
hal-01058939 , version 5 (26-03-2015)

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François Bachoc, Achref Bachouch, Lionel Lenôtre. Hastings-Metropolis algorithm on Markov chains for small-probability estimation. ESAIM: Proceedings, 2015, 48, pp.33. ⟨10.1051/proc/201448013⟩. ⟨hal-01058939v5⟩
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