# GlobalSensitivity.jl: Robust, Fast, and Parallel Global Sensitivity Analysis (GSA) in Julia

Global Sensitivity Analysis (GSA) methods are used to quantify the uncertainty in output of a model with respect to 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 performing global sensitivity analysis using this package is:

GlobalSensitivity.gsaMethod
gsa(f, method::GSAMethod, 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 available GSA methods.
• 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.

source

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.

## Citing

If you use this software in your work, please cite:

@article{dixit2022globalsensitivity,
title={GlobalSensitivity. jl: Performant and Parallel Global Sensitivity Analysis with Julia},
author={Dixit, Vaibhav Kumar and Rackauckas, Christopher},
journal={Journal of Open Source Software},
volume={7},
number={76},
pages={4561},
year={2022}
}

## Reproducibility

The documentation of this SciML package was built using these direct dependencies,
Status ~/work/GlobalSensitivity.jl/GlobalSensitivity.jl/docs/Project.toml
[13f3f980] CairoMakie v0.9.3
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[10745b16] Statistics
and using this machine and Julia version.
Julia Version 1.8.3
Commit 0434deb161e (2022-11-14 20:14 UTC)
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 2 × Intel(R) Xeon(R) CPU E5-2673 v3 @ 2.40GHz
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-13.0.1 (ORCJIT, haswell)
Threads: 1 on 2 virtual cores
A more complete overview of all dependencies and their versions is also provided.
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Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use status --outdated -m
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