  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.
