Introduction to importance sampling in rare-event simulations

Monte Carlo simulations are an important tool in modern-day studies of many physical systems. Where unlikely events are to be simulated, the importanc e sampling technique can considerably ease the processing burdon, without c ompromising statistical significance. Here a comparison of importance sampl ing and standard Monte Carlo simulations is given. Emphasis is on variance reduction, and on the simulation gain of importance sampling, which is calc ulated explicitly for a simple example.