Extension of sample size in Latin Hypercube Sampling with correlated variables

Abstract. In this paper, we suggest principles of a novel simulation method for analyses of functions g (X) of a random vector X, suitable for the cases when the evaluation of g (X) is very expensive. The method is based on Latin Hypercube Sampling strategy. The paper explains how the statistical, sensitivity and reliability analysis of g (X) can be divided into a hierarchical sequence of simulations with (subsets of samples of a random vector X) such that (i) the favourable properties of LHS are retained (low number of simulations needed for significant estimations of statistics of g (X) with a low variability of the estimation); (ii) all subsets can anytime be merged into one set while keeping its consistency (i.e. the simulation process can be halted e.g., when reaching a certain prescribed statistical significance of the estimations). An important aspect of the method is that it efficiently simulates subsets samples of random vectors with focus on their correlation structure. The procedure is quite general and can be applied to other simulation techniques (e.g. crude Monte Carlo, etc.). The method should serve preferably as a tool for very complex and intensive analyses of nonlinear problems g (X) (involving a random/uncertain phenomena) where there is a need for pilot numerical studies, preliminary and subsequently refined estimations of statistics, progressive learning of neural networks or design of experiments.