In this paper, the extended Monte Carlo simulation method is developed for this purpose, which provides four benefits to the parametric global sensitivity analysis and parametric optimization problems. Estimating the functional relation between the probabilistic response of a computational model and the distribution parameters of the model inputs is especially useful for 1) assessing the contribution of the distribution parameters of model inputs to the uncertainty of model output (parametric global sensitivity analysis), and 2) identifying the optimized distribution parameters of model inputs to efficiently and cheaply reduce the uncertainty of model output (parametric optimization).
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