Biasing the transition probabilities in direct Monte Carlo

The mathematical scheme of the biased direct Monte Carlo method is presented in detail and compared with the corresponding biased analogues Monte Carlo method. With reference to the inhomogeneous Poisson processes, an example in the reliability and safety engineering field is given. This refers to sampling from a three-mode Weibull distribution by forcing each of the three modes to be exponential with decay constants 10 times larger than the natural ones. Since the natural distribution under analysis shows a rather uniform behaviour over most of the range of interest, biasing to a uniform distribution has also been investigated. Both examples are shown to lead to a simplification in the sampling procedure and an improvement in the computational efficiency.