Description
MOCQUASIN is an INRIA associated team between Dionysos group at INRIA Rennes - Bretagne Atlantique and the University of Montreal, Canada.
The goal of this team is to compute integrals, sums or to solve equations or optimization problems by means of Monte Carlo methods, which are statisitcal tools usful when the models have a a high complexity (for instance large dimension). They are unavoidable tools in areas such as finance, electronics, sismology, computer science, engineering, physics, transport, biloy, social sciences... Nonetheless, they have the reputation of being slow, i.e. to require a large computational time to reach a given precision. The goal of the project is to work on acceleration techniques, meaning to reach faster the targeted precision. The typical framework is that of rare event simulation for which getting even only one occurence of the event could require a very long time. There are two main acceleration techniques which require a precise calibration depending on the studied model: importance sampling and splitting.
Importance sampling consists in using the ptrobability distribustions driving the system, using laws under which the event becomes more frequent. The estimator is then multiplied by an appropriate factor to it unbiased (the so-called likelihood ratio).
Splitting consists, when simulating the stochastic process, in eliminating the trajectories that seem to go in the wrong direction and cloning (or splitting) those which go towards the rare event. Here again, the estimation has to be pondered by a factor to keep the estimator unbiased.
In both cases, the difficulty is to determine the good strategies in order to obtain a robust estimator when rarity increases. Our goal is to design such robust methods and to apply them to problems encountered in telecommunication and dependability analysis. A combination with the faster randomized quasi-Monte Carlo methods is also a challenge we want to address.
