Correlation control in small-sample Monte Carlo type simulations I: A simulated annealing approach

The objective of this paper is to propose an effective procedure for sampling from a multivariate population within the framework of Monte Carlo simulations. The typical application of the proposed approach involves a computer-based model, featuring random variables, in which it is impossible to find a way (closed form or numerical) to carry out the necessary transformation of the variables, and where simulation is expensive in terms of computing resources and time. Other applications of the proposed method can be seen in random field simulations, optimum learning sets for neural networks and response surfaces, and in the design of experiments.The paper presents a technique for efficient Monte Carlo type simulation of samples of random vectors with prescribed marginals and a correlation structure. It is shown that if the technique is applied for small-sample simulation with a variance reduction technique called Latin Hypercube Sampling, the outcome is a set of samples that match user-defined marginals and covariances. Such a sample is expected to lead to stable estimates of the statistics of the analyzed function, with low variability. The method is very flexible in terms of the allowable combination of marginal distributions and correlation structures. The efficiency of the technique is documented using simple numerical examples. The advantages of the presented method are its simplicity and clarity; the method has proven itself to be simple to use, fast, robust and efficient, especially for very small sample sizes.