# Global Sensitivity Analysis

Global Sensitivity Analysis (GSA) methods are used to quantify the uncertainty in output of a model w.r.t. the parameters. These methods allow practitioners to measure both parameter's individual contributions and the contribution of their interactions to the output uncertainity.

## Installation

To use this functionality, you must install GlobalSensitivity.jl:

]add GlobalSensitivity
using GlobalSensitivity

Note: GlobalSensitivity.jl is unrelated to the GlobalSensitivityAnalysis.jl package.

## General Interface

The general interface for calling a global sensitivity analysis is:

res = gsa(f, method, param_range; samples, batch=false)

where:

• y=f(x) is a function that takes in a single vector and spits out a single vector or scalar. If batch=true, then f takes in a matrix where each row is a set of parameters, and returns a matrix where each row is a the output for the corresponding row of parameters.
• method is one of the GSA methods below.
• param_range is a vector of tuples for the upper and lower bound for the given parameter i.
• samples is a required keyword argument for the number of samples of parameters for the design matrix. Note that this is not relevant for Fractional Factorial Method and Morris Method.

For Delta Moment-Independent Method, EASI Method and Regression Method input and output matrix based method as follows is available:

res = gsa(X, Y, method)

where:

• X is the number of parameters * samples matrix with parameter values.
• Y is the output dimension * number of samples matrix with out evaluated at X's columns.
• method is one of the GSA methods below.

For Sobol Method one can use the following design matrices based method instead of parameter range based method discussed earlier:

effects = gsa(f, method, A, B; batch=false)

where A and B are design matrices with each row being a set of parameters. Note that generate_design_matrices from QuasiMonteCarlo.jl can be used to generate the design matrices.

The descriptions of the available methods can be found in the Methods section. The GSA interface allows for utilizing batched functions with the batch kwarg discussed above for parallel computation of GSA results.