AVaN Pack: An Analytical/Numerical Solution for Variance-Based Sensitivity Analysis

TL;DR

This paper introduces AVaN Pack, a set of JavaScript tools providing an analytical, rather than sampling-based, approach to variance-based sensitivity analysis, specifically Sobol indices, for more precise parameter influence assessment.

Contribution

It presents an innovative analytical solution for variance-based sensitivity analysis, implemented in accessible JavaScript programs, diverging from traditional sampling methods.

Findings

Developed two JavaScript programs for sensitivity analysis

Provided an analytical alternative to sampling-based methods

Enhanced accuracy and efficiency in parameter influence estimation

Abstract

Sensitivity analysis is an important concept to analyze the influences of parameters in a system, an equation or a collection of data. The methods used for sensitivity analysis are divided into deterministic and statistical techniques. Generally, deterministic techniques analyze fixed points of a model whilst stochastic techniques analyze a range of values. Deterministic methods fail in analyze the entire range of input values and stochastic methods generate outcomes with random errors. In this manuscript, we are interested in stochastic methods, mainly in variance-based techniques such as Variance and Sobol indices, since this class of techniques is largely used on literature. The objective of this manuscript is to present an analytical solution for variance based sensitive analysis. As a result of this research, two small programs were developed in Javascript named as AVaN Pack (Analysis of Variance through Numerical solution). These programs allow users to find the contribution of each individual parameter in any function by means of a mathematical solution, instead of sampling-based ones.