PyMC

PyMC (formerly known as PyMC3) is a probabilistic programming language written in Python. It can be used for Bayesian statistical modeling and probabilistic machine learning.

PyMC

Original author(s)	PyMC Development Team
Initial release	May 4, 2013 (2013-05-04)
Stable release	5.22[1]  / 3 April 2025; 13 days ago (3 April 2025)
Repository	https://github.com/pymc-devs/pymc
Written in	Python
Operating system	Unix-like, Mac OS X, Microsoft Windows
Platform	Intel x86 – 32-bit, x64
Type	Statistical package
License	Apache License, Version 2.0
Website	www.pymc.io

PyMC performs inference based on advanced Markov chain Monte Carlo and/or variational fitting algorithms.^{[2] [3][4][5][6]} It is a rewrite from scratch of the previous version of the PyMC software.^[7] Unlike PyMC2, which had used Fortran extensions for performing computations, PyMC relies on PyTensor, a Python library that allows defining, optimizing, and efficiently evaluating mathematical expressions involving multi-dimensional arrays. From version 3.8 PyMC relies on ArviZ to handle plotting, diagnostics, and statistical checks. PyMC and Stan are the two most popular probabilistic programming tools.^[8] PyMC is an open source project, developed by the community and has been fiscally sponsored by NumFOCUS.^[9]

PyMC has been used to solve inference problems in several scientific domains, including astronomy,^[10][11] epidemiology,^[12][13] molecular biology,^[14] crystallography,^[15][16] chemistry,^[17] ecology^[18][19] and psychology.^[20] Previous versions of PyMC were also used widely, for example in climate science,^[21] public health,^[22] neuroscience,^[23] and parasitology.^[24][25]

After Theano announced plans to discontinue development in 2017,^[26] the PyMC team evaluated TensorFlow Probability as a computational backend,^[27] but decided in 2020 to fork Theano under the name Aesara.^[28] Large parts of the Theano codebase have been refactored and compilation through JAX^[29] and Numba were added. The PyMC team has released the revised computational backend under the name PyTensor and continues the development of PyMC.^[30]

Inference engines

PyMC implements non-gradient-based and gradient-based Markov chain Monte Carlo (MCMC) algorithms for Bayesian inference and stochastic, gradient-based variational Bayesian methods for approximate Bayesian inference.

• MCMC-based algorithms:
  • No-U-Turn sampler^[31] (NUTS), a variant of Hamiltonian Monte Carlo and PyMC's default engine for continuous variables
  • Metropolis–Hastings, PyMC's default engine for discrete variables
  • Sequential Monte Carlo for static posteriors
  • Sequential Monte Carlo for approximate Bayesian computation
• Variational inference algorithms:
  • Black-box Variational Inference^[32]

See also

• Stan is a probabilistic programming language for statistical inference written in C++
• ArviZ a Python library for exploratory analysis of Bayesian models
• Bambi is a high-level Bayesian model-building interface based on PyMC