Adaptive Importance Sampling Monte

Another procedure to overcome the inefficiency of Metropolis Monte Carlo is adaptive importance sampling.194-196 In this technique, the partition function (and quantities derived from it, such as the probability of a given conformation) is evaluated by continually upgrading the distribution function (ultimately to the Boltzmann distribution) to concentrate the sampling in the region (s) where the probabilities are highest. 

The statistical error of such sampling is proportional to 1 / /N. Therefore, the accuracy of the method increases with the sample size. More advanced adaptive Monte Carlo methods use, for instance, importance sampling to enhance the convergence and the accuracy over that of the basic Monte Carlo integration. 

This Iterative Fast Monte Carlo (IFM) procedure [20] utilizes the results obtained from Importance sampling to adapt the sampling density to the specific problem. As stated above, the standard error of the estimated failure probability reduces to zero, If the sampHng density hytii) Is chosen to be the original density conditional on the failure domain Of... 

This section discussed a variety of simulation techniques to estimate structural reliability. Topics such as Monte Carlo sampling, importance sampling, and stratified sampling were discussed in detail, and some other advanced topics such as adaptive sampling, variance... 

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