Fortunately, incidents like extreme weather, earthquakes or massive power grid blackouts are a rare occurrence. Analysing properly how likely such rare incidents are to happen can be very valuable, but also very challenging. In his PhD thesis, CWI researcher Krzysztof Bisewski developed mathematical methods that greatly speed up simulations for estimating the probability of rare events. Bisewski defended his thesis Rare Event Simulation and Time Discretization at the University of Amsterdam.

We don’t see extreme weather, major bankruptcies, earthquakes or simultaneous failure of multiple machine components happen every day. Still, if a rare event does occur, it can have an extremely big impact. Knowing how likely such events are to happen, can help prepare for it, or even prevent it from happening. But how can you estimate the probability of extreme events that might have a one in a million chance of happening?**Estimating probabilities**

CWI researcher Krzysztof Bisewski developed methods which make such estimations far more efficient. "A naive way to estimate the probability of an event is to repeatedly simulate the system you’re interested in, and just see how often the event has happened", says Bisewski. "When you want to estimate the likelihoods of events which happen, for instance, one in a million times, you need about a million simulations just to observe that event once. In fact, you need many times more than that to estimate that probability accurately."**Boosting computational efficiency**

The problem is that such simulations require a lot of computational time. Making over a million simulations is practically impossible, as it can take years to complete. Bisewski: "The methods described in my thesis can boost computational efficiency by several orders of magnitude, making it feasible to estimate such probabilities."**Easy to use**

In his thesis, Bisewski developed a new algorithm for estimation of small probabilities, associated with how often an extreme event occurs over very long time periods. It deals with extreme events as simulated with a random system. With this algorithm, it is possible to estimate the likelihood of an extreme event, e.g. one in a million times, without having to do many millions of simulations with the model. Bisewski: "The algorithm is easy to use in practice and does not require detailed knowledge of the process. It can be applied to a broad variety of systems." Right now the algorithm has been successfully applied to a model that shares some characteristics with complex climate models.

Bisewski performed his PhD research at CWI’s Scientific Computing group. His research was supervised by Daan Crommelin (CWI), Michel Mandjes (University of Amsterdam), and Harry van Zanten (Vrije Universiteit Amsterdam).