ABSTRACT
This chapter focuses on the use of importance sampling techniques in rare event simulation. The rejection method serves as a basis for a variety of simulation algorithms of the importance sampling class of algorithms. These algorithms can be used to evaluate expected values of functional with high precision. They form the core of the sequential Monte Carlo methods and of the mean field particle integration theory. Applications of the techniques for precise evaluation of tail probabilities, or, similarly, in rare event simulation. Buffon's needle problem is one of the oldest Monte Carlo integration problems posed in the eighteenth century by Georges-Louis Leclerc, Comte de Buffon. A Youtube video by Dr Tony Padilla illustrates this experiment using 163 matches. The importance sampling technique is closely related to the rejection method.
