Monte Carlo/Monte Carlo Markov Chain Method

Abstract The Monte Carlo simulation is a versatile method for analyzing the behavior of some activities, plans, or processes that involve uncertainty. The method was invented by scientists working on the atomic bomb in the 1940s. It uses randomness to obtain random variable estimates, similarly to the gambling process. A Monte Carlo simulation is a parametric procedure, where specific distributional parameters are required before a simulation can begin. In its simplest form, it can be considered to be a random number generator that is useful for forecasting, estimation, and risk analysis. The Markov Chain Monte Carlo method is more efficient than simple Monte Carlo in obtaining samples for any target distribution and achieving more general inferential objectives.