Multivariate Global Sensitivity Analysis Based on Distance Components Decomposition

Abstract

In this article, a new set of multivariate global sensitivity indices based on distance components decomposition is proposed. The proposed sensitivity indices can be considered as an extension of the traditional variance-based sensitivity indices and the covariance decomposition-based sensitivity indices, and they have similar forms. The advantage of the proposed sensitivity indices is that they can measure the effects of an input variable on the whole probability distribution of multivariate model output when the power of distance 0<α<2. When α=2, the proposed sensitivity indices are equivalent to the covariance decomposition-based sensitivity indices. To calculate the proposed sensitivity indices, an efficient Monte Carlo method is proposed, which can also be used to calculate the covariance decomposition-based sensitivity indices at the same time. The examples show the reasonability of the proposed sensitivity indices and the stability of the proposed Monte Carlo method.

The Influence of Anthropogenic and Environmental Disturbances on Parameter Estimation of a Dengue Transmission Model

“…The SA attempts to determine the contribution of each parameter to the model output uncertainty. For the SA, we chose two variance-based methods from Saltelli et al [ 48 ] and Xiao et al [ 49 ]; these methods were implemented in a Matlab toolbox [ 47 ]. The first method (Saltelli) is particular for scalar model outputs; hence, we used it to quantify the contribution of each parameter to the mean squared error (MSE) function output, i.e., the cost function that quantifies the fit of a given temporal response (from the estimated model parameters) to measured data ( ).…”

Sensitivity, uncertainty and identifiability analyses to define a dengue transmission model with real data of an endemic municipality of Colombia

“…On the other hand, we chose a global approach for SA instead of the local one, because the first attempts to quantify the uncertainty contribution of the model factors in their entire distribution range (space of factors) while the second is only informative for a single point of the space of factors [20]. For this work, we chose a global variance-related SA method proposed in [40] and implemented in the function gsua_sa from GSUA-CSB toolbox [35], which is especially useful for time-response model outputs. Both variance-based and variance-related SA are usually improvements of Sobol [41,42].…”

A novel algorithm for confidence sub-contour box estimation: an alternative to traditional confidence intervals

“…Since both model output and real data are vectors, a general approach to dissimilarity quantification is to define a loss function [14]. It is possible to identify a general form for common loss functions introducing a parameter whose meaning is the importance of the distance between the output vector and the nominal one in a discrete point-to-point comparison sense [23]. A general loss function equation is given in (2), where Y is the output vector obtained when simulating with a specific X, Ŷ is the output vector associated to the real factors X (real data), α is the introduced distance-penalization factor, and |τ | is the number of discrete time elements in τ .…”