Analytic sensitivity analysis for models with correlated input variables

TL;DR

This paper introduces an analytic method using multivariate Taylor series to evaluate how correlated input variables influence the variance of model responses, enabling detailed sensitivity analysis.

Contribution

It presents a novel analytic formula for variance propagation with correlated inputs and derives universal coefficients for decomposing variable contributions.

Findings

Effective validation with numerical examples

Quantifies independent, correlated, and coupling effects

Applied to HIV model sensitivity analysis

Abstract

An analytic formula is proposed to characterize the variance propagation from correlated input variables to the model response, by using multi-variate Taylor series. With the formula, partial variance contributions to the model response are then straightforwardly evaluated in the presence of input correlations. Additionally, an arbitrary variable is represented as the sum of independent and correlated parts. Universal expressions of the coefficients that specify the correlated and independent sections of a single variable are derived by employing linear correlation model. Based on the coefficients, it is nature to quantify the independent, correlated and coupling contributions to the total variance of model response. Numerical examples suggest the effectiveness and validation of our analytic framework for general models. A practical application of the analytic framework is also proposed to the sensitivity analysis of a deterministic HIV model.