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Probabilistic Programming in Python: Bayesian Modeling and Probabilistic Machine Learning with PyTensor

Project description

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PyMC (formerly PyMC3) is a Python package for Bayesian statistical modeling focusing on advanced Markov chain Monte Carlo (MCMC) and variational inference (VI) algorithms. Its flexibility and extensibility make it applicable to a large suite of problems.

Check out the PyMC overview, or one of the many examples! For questions on PyMC, head on over to our PyMC Discourse forum.


  • Intuitive model specification syntax, for example, x ~ N(0,1) translates to x = Normal('x',0,1)

  • Powerful sampling algorithms, such as the No U-Turn Sampler, allow complex models with thousands of parameters with little specialized knowledge of fitting algorithms.

  • Variational inference: ADVI for fast approximate posterior estimation as well as mini-batch ADVI for large data sets.

  • Relies on PyTensor which provides:
    • Computation optimization and dynamic C or JAX compilation

    • NumPy broadcasting and advanced indexing

    • Linear algebra operators

    • Simple extensibility

  • Transparent support for missing value imputation

Getting started

If you already know about Bayesian statistics:

Learn Bayesian statistics with a book together with PyMC

Audio & Video


To install PyMC on your system, follow the instructions on the installation guide.

Citing PyMC

Please choose from the following:

  • DOIpaper PyMC: A Modern and Comprehensive Probabilistic Programming Framework in Python, Abril-Pla O, Andreani V, Carroll C, Dong L, Fonnesbeck CJ, Kochurov M, Kumar R, Lao J, Luhmann CC, Martin OA, Osthege M, Vieira R, Wiecki T, Zinkov R. (2023)

  • DOIzenodo A DOI for all versions.

  • DOIs for specific versions are shown on Zenodo and under Releases


We are using as our main communication channel.

To ask a question regarding modeling or usage of PyMC we encourage posting to our Discourse forum under the “Questions” Category. You can also suggest feature in the “Development” Category.

You can also follow us on these social media platforms for updates and other announcements:

To report an issue with PyMC please use the issue tracker.

Finally, if you need to get in touch for non-technical information about the project, send us an e-mail.


Apache License, Version 2.0

Software using PyMC

General purpose

  • Bambi: BAyesian Model-Building Interface (BAMBI) in Python.

  • calibr8: A toolbox for constructing detailed observation models to be used as likelihoods in PyMC.

  • gumbi: A high-level interface for building GP models.

  • SunODE: Fast ODE solver, much faster than the one that comes with PyMC.

  • pymc-learn: Custom PyMC models built on top of pymc3_models/scikit-learn API

Domain specific

  • Exoplanet: a toolkit for modeling of transit and/or radial velocity observations of exoplanets and other astronomical time series.

  • beat: Bayesian Earthquake Analysis Tool.

  • CausalPy: A package focussing on causal inference in quasi-experimental settings.

Please contact us if your software is not listed here.

Papers citing PyMC

See Google Scholar here and here for a continuously updated list.


See the GitHub contributor page. Also read our Code of Conduct guidelines for a better contributing experience.


PyMC is a non-profit project under NumFOCUS umbrella. If you want to support PyMC financially, you can donate here.

Professional Consulting Support

You can get professional consulting support from PyMC Labs.






Thanks to our contributors


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