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An analytic formula is proposed to characterize the variance propagation fromcorrelated input variables to the model response, by using multi-variate Taylorseries. With the formula, partial variance contributions to the model responseare then straightforwardly evaluated in the presence of input correlations.Additionally, an arbitrary variable is represented as the sum of independentand correlated parts. Universal expressions of the coefficients that specifythe correlated and independent sections of a single variable are derived byemploying linear correlation model. Based on the coefficients, it is nature toquantify the independent, correlated and coupling contributions to the totalvariance of model response. Numerical examples suggest the effectiveness andvalidation of our analytic framework for general models. A practicalapplication of the analytic framework is also proposed to the sensitivityanalysis of a deterministic HIV model.

Analytic sensitivity analysis for models with correlated input variables