List of uncertainty propagation software

List of uncertainty propagation software used to perform propagation of uncertainty calculations:

Software

• ASUE Potent web interface powered by webMathematica to evaluate uncertainty symbolically using GUM. Webpage also allows symbolic uncertainty evaluation via ASUE framework (with reference), which is an extension to GUM framework
• Dempster Shafer with Intervals (DSI) Toolbox is a MATLAB toolbox for verified computing under Dempster–Shafer theory. It provides aggregation rules, fast (non) monotonic function propagation, plots of basic probability assignments, verified fault tree analysis (FTA), and much more.
• EasyGraph is a graphing package that supports error propagation directly into the error bars.
• Epc error propagating calculator (Epc) is an open source script based tool that calculates the propagation of errors in variables. To quote the text on the Epc web page "This is done by repeated calculation of the expression using variable-values which are generated using a random number generator whose mean and standard-deviation match the values specified for the variable".
• Error Calculator Free/libre cross-platform calculator with minimalist interface. Designed for use in practical courses at natural sciences. Exposes all formulae needed to calculate the results, interoperability with office, support for physical quantities with units.
• Error Propagation Calculator Free cross-platform calculator (macOS, Windows, Linux) written in Python. Essentially a GUI interface for the Python Uncertainties library. Easy to use and install.
• ErrorCalc is a scientific calculator app for iPhone or iPad that performs error propagation (Supports Algebraic and RPN modes of entry)
• FuncDesigner
• GUMsim is a Monte Carlo simulator and uncertainty estimator for Windows
• GUM Tree is a design pattern for propagating measurement uncertainty. An implementation exists in R and add-ons for Excel (real and complex numbers).
• GUM Tree Calculator is a programmable Windows command-line tool with full support for uncertainty calculations involving real and complex quantities.
• GUM Workbench implements a systematic way to analyze an uncertainty problem for single and multiple results. GUM + Monte Carlo. Free restricted educational version available.
• The Gustavus propagator is an open source calculator that supports error propagation developed by Thomas Huber.
• The laffers.net propagator is a web based tool for propagating errors in data. The tool uses the standard methods for propagation.
• Mathos Core Library Uncertainty package Open source (.NET targeting library).
• MC-Ed is a native Windows software to perform uncertainty calculations according to the Supplement 1 to the Guide to the expression of uncertainty in measurement using Monte-Carlo method.
• Measurements.jl is a free and open-source error propagation calculator and library. It supports real and complex numbers with uncertainty, arbitrary-precision arithmetic calculations, functional correlation between variables, and mathematical and linear algebra operations with matrices and arrays.
• Metas.UncLib is a C# software library. A MATLAB wrapper exists. It supports: multivariate uncertainties, complex values, correlations, vector, and matrix algebra.
• MUSE Measurement Uncertainty Simulation and Evaluation using the monte carlo method.
• OpenCOSSAN is a MATLAB toolbox for uncertainty propagation, reliability analysis, model updating, sensitivity and robust design optimization. Allows interacting with 3rd party solvers. Interfaces with HPC through GridEngine and OpenLava.
• OpenTURNS is a C++ and Python framework for probabilistic modelling and uncertainty management developed by the OpenTURNS consortium (Airbus, EDF R&D, IMACS, Phimeca). It contains state of the art algorithms for univariate, multivariate and infinite dimensional probabilistic modelling (arithmetic of independent random variables, copulas, Bayesian models, stochastic processes and random fields), Monte Carlo simulation, surrogate modelling (Kriging, functional chaos decomposition, low rank tensor approximation, Karhunen-Loeve decomposition, mixture of experts), rare event estimation (variance reduction, FORM/SORM reliability methods), robust optimization, global sensitivity analysis (ANCOVA, Sobol' indices). It can interact with third party software through a generic Python interface, which also allows to connect HPC facilities.
• QMSys GUM is a potent commercial tool for measurement uncertainty analysis including Monte Carlo simulation for Windows (free restricted educational version available).
• Risk Calc supports probability bounds analysis, standard fuzzy arithmetic, and classical interval analysis for conducting distribution-free or nonparametric risk analyses.
• SmartUQ is a commercial uncertainty quantification and analytics software package. Capabilities include DOE generation, emulator construction, uncertainty propagation, sensitivity analysis, statistical calibration, and inverse analysis.
• SOERP implements second-order error propagation as a free Python library. Calculations are carried out naturally in calculator format and correlations are maintained.
• SCaViS is a free data-analyais program written in Java and supports Python and Groovy.
• The Uncertainty Calculator is a JavaScript browser-based calculator that performs error propagation calculations.
• Uncertainties is a potent free calculator and Python software library for transparently performing calculations with uncertainties and correlations.
• Mathos Laboratory Uncertainty Calculator This is a web interface for uncertainty calculations.
• UQLab is a software framework for uncertainty quantification developed at ETH Zurich. It is a general-purpose software running in MATLAB which contains state-of-the-art methods for Monte Carlo simulation, dependence modelling (copula theory), surrogate modelling (polynomial chaos expansions, Kriging (a.k.a Gaussian process modelling), low-rank tensor approximations, global sensitivity analysis (ANOVA, Sobol’ indices, distribution-based indices), rare event simulation (a.k.a. reliability methods).

Comparison

See also

• Automatic differentiation#Software, also can be used to obtain uncertainties

References

• Y. C. Kuang, A. Rajan, M. P.-L. Ooi, and T. C. Ong (2014), "Standard uncertainty evaluation of multivariate polynomial," Measurement, vol. 58, pp. 483–494, Dec. 2014
• A. Rajan, M. P. Ooi, Y. C. Kuang, and S. N. Demidenko, "Analytical Standard Uncertainty Evaluation Using Mellin Transform," Access, IEEE, vol. 3, pp. 209–222, 2015.
• Auer, E., Luther, W., Rebner, G., Limbourg, P. (2010) A Verified MATLAB Toolbox for the Dempster-Shafer Theory. Proceedings of the Workshop on the Theory of Belief Functions
• Bevington, P.R. and Robinson, D.K. (2002) Data Reduction and Error Analysis for the Physical Sciences, 3rd Ed., McGraw-Hill ISBN 0-07-119926-8
• Ferson, S., Kreinovich, V., Hajagos, J., Oberkampf, W. and Ginzburg, L. (2007) "Experimental Uncertainty Estimation and Statistics for Data Having Interval Uncertainty". Sandia National Laboratories Report: SAND2007-0939.
• Patelli, E., An Open Computational Framework for Reliability Based Optimization, In proceeding of: The Eleventh International Conference on Computational Structures Technology, Dubrovnik, Croatia 4–7 September 2012