The research and simulation about rare events based on MCMC

In this paper, the importance of the rare events has been strengthened and the MCMC (Markov Chain Monte Carlo) sampling is proposed to simulate the possibility of the rare events instead of traditional standard Monte Carlo simulation. Gibbs sampling as one of the popular and widely used algorithm is adopted for MCMC methodology. In the end of this paper, a useful software WinBUGS was introduced to provide some proof for MCMC method based on Gibbs sampling to estimate the possibility of rare events.