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Original author(s)PyMC Development Team
Initial releaseMay 4, 2013 (2013-05-04)
Stable release
v5.15.1[1] Edit this on Wikidata / 30 May 2024; 15 days ago (30 May 2024)
Written inPython
Operating systemUnix-like, Mac OS X, Microsoft Windows
PlatformIntel x86 – 32-bit, x64
TypeStatistical package
License Apache License, Version 2.0

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 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[edit]

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.

See also[edit]

  • Stan is a probabilistic programming language for statistical inference written in C++
  • ArviZ a Python library for Exploratory Analysis of Bayesian Models


  1. ^ "v5.15.1". 30 May 2024. Retrieved 30 May 2024.
  2. ^ 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) PyMC: a modern, and comprehensive probabilistic programming framework in Python. PeerJ Comput. Sci. 9:e1516 doi:10.7717/peerj-cs.1516
  3. ^ Salvatier J, Wiecki TV, Fonnesbeck C. (2016) Probabilistic programming in Python using PyMC3. PeerJ Computer Science 2:e55 doi:10.7717/peerj-cs.55
  4. ^ Martin, Osvaldo (2024). Bayesian Analysis with Python. Packt Publishing Ltd. ISBN 9781805127161. Retrieved 24 February 2024.
  5. ^ Martin, Osvaldo; Kumar, Ravin; Lao, Junpeng (2021). Bayesian Modeling and Computation in Python. CRC-press. pp. 1–420. ISBN 9780367894368. Retrieved 7 July 2022.
  6. ^ Davidson-Pilon, Cameron (2015-09-30). Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference. Addison-Wesley Professional. ISBN 9780133902921.
  7. ^ "documentation". Retrieved 2017-09-20.
  8. ^ "The Algorithms Behind Probabilistic Programming". Retrieved 2017-03-10.
  9. ^ "NumFOCUS Announces New Fiscally Sponsored Project: PyMC3". NumFOCUS | Open Code = Better Science. Retrieved 2017-03-10.
  10. ^ Greiner, J.; Burgess, J. M.; Savchenko, V.; Yu, H.-F. (2016). "On the Fermi-GBM Event 0.4 s after GW150914". The Astrophysical Journal Letters. 827 (2): L38. arXiv:1606.00314. Bibcode:2016ApJ...827L..38G. doi:10.3847/2041-8205/827/2/L38. ISSN 2041-8205. S2CID 3529170.
  11. ^ Hilbe, Joseph M.; Souza, Rafael S. de; Ishida, Emille E. O. (2017-04-30). Bayesian Models for Astrophysical Data: Using R, JAGS, Python, and Stan. Cambridge University Press. ISBN 9781108210744.
  12. ^ Brauner, Jan M.; Mindermann, Sören; Sharma, Mrinank; Johnston, David; Salvatier, John; Gavenčiak, Tom; Stephenson, Anna B.; Leech, Gavin; Altman, George; Mikulik, Vladimir; Norman, Alexander John; Monrad, Joshua Teperowski; Besiroglu, Tamay; Ge, Hong; Hartwick, Meghan A.; Teh, Yee Whye; Chindelevitch, Leonid; Gal, Yarin; Kulveit, Jan (2020-12-15). "Inferring the effectiveness of government interventions against COVID-19". Science. 371 (6531): eabd9338. doi:10.1126/science.abd9338. PMC 7877495. PMID 33323424.
  13. ^ Systrom, Kevin; Vladek, Thomas; Krieger, Mike. "Rt.live Github repository". Rt.live. Retrieved 10 January 2021.
  14. ^ Wagner, Stacey D.; Struck, Adam J.; Gupta, Riti; Farnsworth, Dylan R.; Mahady, Amy E.; Eichinger, Katy; Thornton, Charles A.; Wang, Eric T.; Berglund, J. Andrew (2016-09-28). "Dose-Dependent Regulation of Alternative Splicing by MBNL Proteins Reveals Biomarkers for Myotonic Dystrophy". PLOS Genetics. 12 (9): e1006316. doi:10.1371/journal.pgen.1006316. ISSN 1553-7404. PMC 5082313. PMID 27681373.
  15. ^ Sharma, Amit; Johansson, Linda; Dunevall, Elin; Wahlgren, Weixiao Y.; Neutze, Richard; Katona, Gergely (2017-03-01). "Asymmetry in serial femtosecond crystallography data". Acta Crystallographica Section A. 73 (2): 93–101. doi:10.1107/s2053273316018696. ISSN 2053-2733. PMC 5332129. PMID 28248658.
  16. ^ Katona, Gergely; Garcia-Bonete, Maria-Jose; Lundholm, Ida (2016-05-01). "Estimating the difference between structure-factor amplitudes using multivariate Bayesian inference". Acta Crystallographica Section A. 72 (3): 406–411. doi:10.1107/S2053273316003430. ISSN 2053-2733. PMC 4850660. PMID 27126118.
  17. ^ Garay, Pablo G.; Martin, Osvaldo A.; Scheraga, Harold A.; Vila, Jorge A. (2016-07-21). "Detection of methylation, acetylation and glycosylation of protein residues by monitoring13C chemical-shift changes: A quantum-chemical study". PeerJ. 4: e2253. doi:10.7717/peerj.2253. ISSN 2167-8359. PMC 4963218. PMID 27547559.
  18. ^ Wang, Yan; Huang, Hong; Huang, Lida; Ristic, Branko (2017). "Evaluation of Bayesian source estimation methods with Prairie Grass observations and Gaussian plume model: A comparison of likelihood functions and distance measures". Atmospheric Environment. 152: 519–530. Bibcode:2017AtmEn.152..519W. doi:10.1016/j.atmosenv.2017.01.014.
  19. ^ MacNeil, M. Aaron; Chong-Seng, Karen M.; Pratchett, Deborah J.; Thompson, Casssandra A.; Messmer, Vanessa; Pratchett, Morgan S. (2017-03-14). "Age and Growth of An Outbreaking Acanthaster cf. solaris Population within the Great Barrier Reef" (PDF). Diversity. 9 (1): 18. doi:10.3390/d9010018.
  20. ^ Tünnermann, Jan; Scharlau, Ingrid (2016). "Peripheral Visual Cues: Their Fate in Processing and Effects on Attention and Temporal-Order Perception". Frontiers in Psychology. 7: 1442. doi:10.3389/fpsyg.2016.01442. ISSN 1664-1078. PMC 5052275. PMID 27766086.
  21. ^ Graham, Nicholas A. J.; Jennings, Simon; MacNeil, M. Aaron; Mouillot, David; Wilson, Shaun K. (2015). "Predicting climate-driven regime shifts versus rebound potential in coral reefs". Nature. 518 (7537): 94–97. Bibcode:2015Natur.518...94G. doi:10.1038/nature14140. PMID 25607371. S2CID 4453338.
  22. ^ Mascarenhas, Maya N.; Flaxman, Seth R.; Boerma, Ties; Vanderpoel, Sheryl; Stevens, Gretchen A. (2012-12-18). "National, Regional, and Global Trends in Infertility Prevalence Since 1990: A Systematic Analysis of 277 Health Surveys". PLOS Medicine. 9 (12): e1001356. doi:10.1371/journal.pmed.1001356. ISSN 1549-1676. PMC 3525527. PMID 23271957.
  23. ^ Cavanagh, James F; Wiecki, Thomas V; Cohen, Michael X; Figueroa, Christina M; Samanta, Johan; Sherman, Scott J; Frank, Michael J (2011). "Subthalamic nucleus stimulation reverses mediofrontal influence over decision threshold". Nature Neuroscience. 14 (11): 1462–1467. doi:10.1038/nn.2925. PMC 3394226. PMID 21946325.
  24. ^ Gething, Peter W.; Elyazar, Iqbal R. F.; Moyes, Catherine L.; Smith, David L.; Battle, Katherine E.; Guerra, Carlos A.; Patil, Anand P.; Tatem, Andrew J.; Howes, Rosalind E. (2012-09-06). "A Long Neglected World Malaria Map: Plasmodium vivax Endemicity in 2010". PLOS Neglected Tropical Diseases. 6 (9): e1814. doi:10.1371/journal.pntd.0001814. ISSN 1935-2735. PMC 3435256. PMID 22970336.
  25. ^ Pullan, Rachel L.; Smith, Jennifer L.; Jasrasaria, Rashmi; Brooker, Simon J. (2014-01-21). "Global numbers of infection and disease burden of soil transmitted helminth infections in 2010". Parasites & Vectors. 7: 37. doi:10.1186/1756-3305-7-37. ISSN 1756-3305. PMC 3905661. PMID 24447578.
  26. ^ Lamblin, Pascal (28 September 2017). "MILA and the future of Theano". theano-users (Mailing list). Retrieved 28 September 2017.
  27. ^ Developers, PyMC (2018-05-17). "Theano, TensorFlow and the Future of PyMC". PyMC Developers. Retrieved 2019-01-25.
  28. ^ "The Future of PyMC3, or: Theano is Dead, Long Live Theano". PyMC Developers. 27 October 2020. Retrieved 10 January 2021.
  29. ^ Bradbury, James; Frostig, Roy; Hawkins, Peter; James, Matthew James; Leary, Chris; Maclaurin, Dougal; Necula, George; Paszke, Adam; VanderPlas, Jake; Wanderman-Milne, Skye; Zhang, Qiao. "JAX". GitHub. Retrieved 10 January 2021.
  30. ^ "PyMC Timeline". PyMC Timeline. Retrieved 10 January 2021.
  31. ^ Hoffman, Matthew D.; Gelman, Andrew (April 2014). "The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo". Journal of Machine Learning Research. 15: pp. 1593–1623.
  32. ^ Kucukelbir, Alp; Ranganath, Rajesh; Blei, David M. (June 2015). "Automatic Variational Inference in Stan". 1506 (3431). arXiv:1506.03431. Bibcode:2015arXiv150603431K. {{cite journal}}: Cite journal requires |journal= (help)

Further reading[edit]

  • Martin, Osvaldo (2024). Bayesian Analysis with Python : A Practical Guide to Probabilistic Modeling (Third ed.). Packt. ISBN 978-1-80512-716-1.

External links[edit]

  • PyMC website
  • PyMC source, a Git repository hosted on GitHub
  • PyTensor is a Python library for defining, optimizing, and efficiently evaluating mathematical expressions involving multi-dimensional arrays.