Optimisation of interacting particle systems for rare event estimation

The interacting particle system (IPS) is a recent probabilistic model proposed to estimate rare event probabilities for Markov chains. The principle of IPS is to apply alternatively selection and mutation stages to a set of initial particles in order to estimate probabilities or quantiles more accurately than with usual estimation techniques. The practical issue of IPS is the tuning of a parameter in the selection stage. Kriging-based optimisation strategy with a low simulation cost is thus proposed in order to minimise the probability estimate relative error. The efficiency of the proposed strategy is demonstrated on different test cases.