Scientific computations are surrounded by various forms of uncertainty, requiring appropriate treatment to maximise the credibility of computations. Empirical information is often scarce, vague, conflicting and imprecise, requiring expressive uncertainty structures for trustful representation, aggregation and propagation.

This package is underpinned by a framework of uncertain number which allows for a closed computation ecosystem whereby trustworthy computations can be conducted in a rigorous manner. It provides capabilities across the typical uncertainty analysis pipeline, encompassing characterisation, aggregation, propagation, model updating, and applications including reliability analysis and optimisation under uncertainty, especially with a focus on imprecise probabilities.

Uncertain Number refers to a generalised representation that unifies several uncertainty constructs including real numbers, intervals, probability distributions, interval bounds on probability distributions (i.e. probability boxes), and finite DempsterShafer structures. It is mostly suitable for managing mixed types of uncertainties.

Getting started

Explore the documentation to get started, featuring hands-on tutorials and in-depth examples that showcase the power of the package.

pyuncertainnumber exposes APIs at different levels. It features high-level APIs best suited for new users to quickly start with uncertainty computations with uncertain numbers, and also low-level APIs allowing experts to have additional controls over mathematical constructs such as p-boxes, Dempster Shafer structures, probability distributions, etc.

Installation

PyUncertainNumber can be installed from PyPI. Upon activation of your virtual environment, use the code below in your terminal. For additional instructions, refer to installation guide.

pip install pyuncertainnumber

Capabilities

• PyUncertainNumber is a Python package for generic computational tasks focussing on rigorous uncertainty analysis, which provides a research-grade computing environment for uncertainty characterisation, propagation, validation and uncertainty extrapolation.
• PyUncertainNumber supports probability bounds analysis to rigorously bound the prediction for the quantity of interest with mixed uncertainty propagation.
• PyUncertainNumber also features great natural language support as such characterisatin of input uncertainty can be intuitively done by using natural language like about 7 or simple expression like [15 +- 10%], without worrying about the elicitation.
• Interoperability via serialization: features the save and loading of Uncertain Number objects to work with downstream applications.
• Yields informative results during the computation process such as the combination that leads to the maximum in vertex method.

UQ multiverse

UQ is a big world (like Marvel multiverse) consisting of abundant theories and software implementations on multiple platforms. Some notable examples include OpenCossan UQlab in Matlab and ProbabilityBoundsAnalysis.jl in Julia, and many others of course. We focus mainly on the imprecise probability frameworks. PyUncertainNumber is rooted in Python and has close ties with the Python scientific computing ecosystem, it builds upon and greatly extends a few pioneering projects, such as intervals, scipy-stats and pba-for-python to generalise probability and interval arithmetic. Beyond arithmetic calculations, PyUncertainNumber has offered a wide spectrum of algorithms and methods for uncertainty characterisation, propagation, surrogate modelling, and optimisation under uncertainty, allowing imprecise uncertainty analysis in both intrusive and non-intrusive manner. PyUncertainNumber is under active development and will continue to be dedicated to support imprecise analysis in engineering using Python.

Citation

Yu Chen, Scott Ferson (2025). Imprecise uncertainty management with uncertain numbers to facilitate trustworthy computations., SciPy proceedings 2025.

A downloadable version can be accessed here.

@inproceedings{chen2025scipyproceed,
  title = {Imprecise uncertainty management with uncertain numbers to facilitate trustworthy computations},
  booktitle = {SciPy Proceedings},
  year = {2025},
  author = {Chen, Yu and Ferson, Scott},
  doi = {10.25080/ahrt5264}
}

@software{chen_2025_17235456,
  author       = {Chen, (Leslie) Yu},
  title        = {PyUncertainNumber},
  publisher    = {Zenodo},
  version      = {0.1.1},
  doi          = {10.5281/zenodo.17235456},
  url          = {https://doi.org/10.5281/zenodo.17235456},
}