Sensitivity analysis (SA) is one of the main themes of the Water Programming Blog. There are several decent blog posts that go over theoretical aspects of sensitivity analysis (for example, here , here, and here). Also, many blog posts explain how to efficiently and elegantly visualize sensitivity analysis results (for example, here, and here). In addition, there are many blog posts related to SALib, a widely used Python library developed at Cornell University by former members of Dr. Reed research group (for example, here, here, and here).

Recently, I have been trying to put together a comprehensive list of other SA tools, and I thought it might be useful to write a blog post on this topic. I organized the following list based on the platforms I have explored so far, including MATLAB, Python, and R. After that, I will introduce some other open-source and commercialized SA tools.

MATLAB

Many MATLAB packages have been developed to perform sensitivity analysis and uncertainty quantification. As the following table shows, they have been created by a variety of universities and research institutes. Also, several of them cover different sensitivity analysis methods, such as Regression-based SA, Variance-based SA (e.g., Sobol), and derivative-based SA. All of them support at least two sampling techniques, such as Latin Hyper Cube Sampling. Many of them are generic (discipline-free) and can be used to answer different types of questions; however, a few of them (e.g., PeTTSy and DyGloSA) have been tailored to specific applications, such as biological models. Also, almost all of them include some post-processing and visualization components.

There are two toolboxes that work in platforms other than MATLAB. The SAFE package developed by Pianosi et al. (2015) has R and Python versions, and the SaSAT package developed at the University of New South Wales works in Microsoft Excel.

Abbreviation	Full Name	Example of Methods Supported	Institution
GSAT	Global Sensitivity Analysis Toolbox	Sobol and FAST	MATLAB
SAFE	Sensitivity Analysis For Everybody	EET, or Morris method,RSA, Sobol, FAST, and PAWN	University of Bristol
GSUA	Global Sensitivity and Uncertainty Analysis Toolbox	Sobol	MATLAB
GUI-HDMR	Global Sensitivity Analysis Toolbox	Global Sensitivity Analysis using HDMR	University of Leeds
DyGloSA	Dynamical Global Sensitivity Analysis Toolbox	Dynamical Global parameter Sensitivity Analysis (GPSA) of ODE models	University of Luxembourg
PeTTSy	Perturbation Theory Toolbox for Systems	Perturbation analysis of complex systems biology models	University of Cambridge
SaSAT	Sampling and Sensitivity Analysis Tools	Regression-based (Pearson, Spearman, and Partial Rank Correlation Coefficients)	The University of New South Wales
SensSB	Sensitivity Analysis in Systems Biology models	Local SA, derivative and variance based global sensitivity analysis	Process Engineering Group at IIM-CSIC (Vigo, Spain)
SobolGSA	Global Sensitivity Analysis and Metamodeling Software	Morris, Sobol FAST and derivative-based	Imperial College London
SUMO	SUrrogate Modeling Toolbox	Surrogate models, sensitivity analysis	Ghent University
UQLab	The Framework for Uncertainty Quantification	Morris, Kucherenko,ANCOVA, Borgonovo, Sobol	ETH Zurich

Python

Interestingly, I was not able to find many Python libraries, and most of the ones that I did find were developed for specific applications. Please leave a comment if you are aware of any other packages that have not been listed here. Among these packages, SALib seems to be the one that covers more SA and sampling methods. There are two SA and QU packages that have C++ versions (OpenTURNS and UQTk). Also, uncertainpy have been originally developed for neuroscience applications.

Abbreviation	Description	Example of Methods Supported	Institution
SALib	Python sensitivity analysis library	Sobol, Morris, FAST, RBD-FAST, Delta Moment-Independent Measure, Derivative-based, Factorial	Cornell University
uncertainpy	Uncertainty quantification and sensitivity analysis library	Sobol	University of Oslo
MATK	Model analysis toolKit	FAST, Sobol	Los Alamos National Laboratory
UQTk	Quantification of uncertainty in numerical models	Sobol	Sandia National Lab
OpenTURNS	Open source initiative for the Treatment of Uncertainties	Spearman Correlation Coefficients, Sobol, ANCOVA, UQ	Technical University of Denmark
varsens	Variance Based Sensitivity Analysis	Sobol	Vanderbilt University

R

I was able to find about fifty R packages that have sensitivity analysis features. The following table lists the ones that have the most comprehensive SA functionalities. It seems that the rest of them were developed for specific areas of science and have limited SA functionality. I list some of these here (RMut, pksensi, ivmodel, FME, episensr, pse).

Based on what I found, sensitivity package seems to cover a wider range of SA methods. Reader can refer to this blog post for more information about the sensitivity package.

Name	Example of Methods Supported
sensobol	Third-order Sobol
sensitivity	Sobol, Morris, FAST, RBD-FAST, Delsa, Derivative-based , Factorial
ODEsensitivity	Morris, Sobol
multisensi	SA on models with multivariate outputs
konfound	Robustness and sensitivity of empirical models
fast	FAST
BASS	Sobol

Other Platforms

There are many other SA tools that have been developed in other platforms, and the following table lists only a few of them. There are also several commercial SA platforms such as SDI, VISYOND, and SMARTUQ that seem to have nice graphical user interfaces (GUIs), but, because they are not freeware and the source codes are not available, they might have limited applications in academic research.

Abbreviation	Main applications	Programming Language	Institution
Dakota	Optimization, QU, SA (Sobol, FAST, Morris)	C++	Sandia National Laboratory
PSUADE	QU, Spearman, Pearson Correlation Coefficient, Sobol,  Morris, FAST	C++	Lawrence Livermore National Laboratory
SIMLab	Sobol, FAST, Morris	GUI-based	The European Commission’s science and knowledge service

Please leave a comment and let me know if you are aware of any other useful tools that I did not list here.