PyMC

**PyMC**
原作者	PyMC开发团队
首次发布	2013年5月4日
当前版本	5.13.1 (2024年4月15日；穩定版本);
源代码库	https://github.com/pymc-devs/pymc
编程语言	Python
操作系统	类Unix, Mac OS X, Microsoft Windows
平台	Intel x86 – 32-bit, x64
类型	统计包（英语：List of statistical software）
许可协议	Apache License, Version 2.0
网站	www.pymc.io

PyMC（曾叫做PyMC3^[2]）是一个Python包，用于贝叶斯统计建模和概率机器学习，它聚焦于高级马尔可夫链蒙特卡洛法和变分拟合算法^[3]^[4]^[5]。

概述

PyMC曾经叫做PyMC3，不同于早先的使用Fortran扩展进行计算的PyMC2，它依靠Theano来进行自动微分、计算优化和动态C语言编译^[4]^[6]。从版本3.8开始PyMC依据ArviZ（英语：ArviZ）来进行数据可视化和贝叶斯推断的探索分析（英语：Exploratory data analysis）^[7]。PyMC和Stan（英语：Stan (software)）是两个最流行的概率编程工具^[8]。

PyMC是开源项目，由社区开发并在财务上得到NumFocus赞助^[9]。PyMC已经在很多领域中被用于解决推断问题，包括天文学^[10]^[11]、流行病学^[12]^[13]、分子生物学^[14]、晶体学^[15]^[16]、化学^[17]、生态学^[18]^[19]和心理学^[20]。

在Theano于2017年宣布计划停止开发之后^[21]，PyMC团队曾评估采用TensorFlow Probability^[22]作为计算后端^[23]，但是在2020年接管Theano的开发^[24]。在2021年1月绝大部份的Theano代码基被重新建造，并增加了通过JAX和Numba的编译，修订后的这个计算后端以新名字Aesara发行。PyMC团队在2021年6月将PyMC3更名为PyMC^[2]。2022年11月28日，PyMC团队宣布采用从Aesara计划分叉出PyTensor^[25]。

推论引擎

PyMC实现了不基于梯度的和基于梯度的马尔可夫链蒙特卡洛（MCMC）算法用于贝叶斯推断和随机（Stochastic（英语：Stochastic）），基于梯度的变分贝叶斯方法（英语：variational Bayesian methods）用于近似贝叶斯推断。

MCMC算法：
- No-U-Turn采样（NUTS）^[26]，是哈密顿蒙特卡洛（英语：Hamiltonian Monte Carlo）的变体和PyMC3用于连续变量的缺省引擎。
- 梅特罗波利斯-黑斯廷斯算法，是PyMC3用于离散变量的缺省引擎。
- 顺序蒙特卡洛算法。
变分推断算法：
- 黑箱变分推断^[27]。

参见

Stan（英语：Stan (software)）是用C++编写统计推论的概率编程语言。

引用

^ v5.13.1. 2024年4月15日 [2024年4月18日].
^ ^2.0 ^2.1 PyMC Timeline. PyMC Timeline. [2021-01-20]. （原始内容存档于2018-05-20）.
^ Salvatier J, Wiecki TV, Fonnesbeck C. (2016) Probabilistic programming in Python using PyMC3. PeerJ Computer Science 2:e55 https://doi.org/10.7717/peerj-cs.55
^ ^4.0 ^4.1 Martin, Osvaldo. Bayesian Analysis with Python. Packt Publishing Ltd. 2016: 31–60 [16 September 2017]. ISBN 9781785889851 （英语）.
^ Davidson-Pilon, Cameron. Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference. Addison-Wesley Professional. 2015-09-30. ISBN 9780133902921 （英语）.
^ Hilpisch, Yves. Python for Finance: Analyze Big Financial Data. O'Reilly Media, Inc. 2014-12-11. ISBN 9781491945391 （英语）.
^ ArviZ — Exploratory analysis of Bayesian models. [2023-09-21]. （原始内容存档于2023-10-11）.
^ The Algorithms Behind Probabilistic Programming. [2017-03-10]. （原始内容存档于2021-01-29）.
^ NumFOCUS Announces New Fiscally Sponsored Project: PyMC3. NumFOCUS | Open Code = Better Science. [2017-03-10]. （原始内容存档于2017-09-21）.
^ Greiner, J.; Burgess, J. M.; Savchenko, V.; Yu, H.-F. On the Fermi-GBM Event 0.4 s after GW150914. The Astrophysical Journal Letters. 2016, 827 (2): L38. Bibcode:2016ApJ...827L..38G. ISSN 2041-8205. arXiv:1606.00314 . doi:10.3847/2041-8205/827/2/L38 （英语）.
^ Hilbe, Joseph M.; Souza, Rafael S. de; Ishida, Emille E. O. Bayesian Models for Astrophysical Data: Using R, JAGS, Python, and Stan. Cambridge University Press. 2017-04-30 [2021-01-20]. ISBN 9781108210744. （原始内容存档于2021-02-03）（英语）.
^ 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. Inferring the effectiveness of government interventions against COVID-19. Science. 2020-12-15 [2021-01-20]. doi:10.1126/science.abd9338. （原始内容存档于2021-02-07）.
^ Systrom, Kevin; Vladek, Thomas; Krieger, Mike. Rt.live Github repository. Rt.live. [10 January 2021]. （原始内容存档于2021-01-06）.
^ 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. Dose-Dependent Regulation of Alternative Splicing by MBNL Proteins Reveals Biomarkers for Myotonic Dystrophy. PLOS Genetics. 2016-09-28, 12 (9): e1006316. ISSN 1553-7404. PMC 5082313 . PMID 27681373. doi:10.1371/journal.pgen.1006316.
^ Sharma, Amit; Johansson, Linda; Dunevall, Elin; Wahlgren, Weixiao Y.; Neutze, Richard; Katona, Gergely. Asymmetry in serial femtosecond crystallography data. Acta Crystallographica Section A. 2017-03-01, 73 (2): 93–101. ISSN 2053-2733. PMC 5332129 . PMID 28248658. doi:10.1107/s2053273316018696 （英语）.
^ Katona, Gergely; Garcia-Bonete, Maria-Jose; Lundholm, Ida. Estimating the difference between structure-factor amplitudes using multivariate Bayesian inference. Acta Crystallographica Section A. 2016-05-01, 72 (3): 406–411. ISSN 2053-2733. PMC 4850660 . PMID 27126118. doi:10.1107/S2053273316003430 （英语）.
^ Garay, Pablo G.; Martin, Osvaldo A.; Scheraga, Harold A.; Vila, Jorge A. Detection of methylation, acetylation and glycosylation of protein residues by monitoring13C chemical-shift changes: A quantum-chemical study. PeerJ. 2016-07-21, 4: e2253. ISSN 2167-8359. PMC 4963218 . PMID 27547559. doi:10.7717/peerj.2253 （英语）.
^ Wang, Yan; Huang, Hong; Huang, Lida; Ristic, Branko. Evaluation of Bayesian source estimation methods with Prairie Grass observations and Gaussian plume model: A comparison of likelihood functions and distance measures. Atmospheric Environment. 2017, 152: 519–530. Bibcode:2017AtmEn.152..519W. doi:10.1016/j.atmosenv.2017.01.014.
^ MacNeil, M. Aaron; Chong-Seng, Karen M.; Pratchett, Deborah J.; Thompson, Casssandra A.; Messmer, Vanessa; Pratchett, Morgan S. Age and Growth of An Outbreaking Acanthaster cf. solaris Population within the Great Barrier Reef. Diversity. 2017-03-14, 9 (1): 18. doi:10.3390/d9010018 （英语）.
^ Tünnermann, Jan; Scharlau, Ingrid. Peripheral Visual Cues: Their Fate in Processing and Effects on Attention and Temporal-Order Perception. Frontiers in Psychology. 2016, 7. ISSN 1664-1078. PMC 5052275 . PMID 27766086. doi:10.3389/fpsyg.2016.01442 （英语）.
^ Lamblin, Pascal. MILA and the future of Theano. theano-users (邮件列表). 28 September 2017 [28 September 2017]. （原始内容存档于2011-01-22）.
^ TensorFlow Probability is a library for probabilistic reasoning and statistical analysis. [2022-08-31]. （原始内容存档于2022-09-04）.
^ Developers, PyMC. Theano, TensorFlow and the Future of PyMC. PyMC Developers. 2018-05-17 [2019-01-25]. （原始内容存档于2020-08-06）.
^ The Future of PyMC3, or: Theano is Dead, Long Live Theano. PyMC Developers. [10 January 2021]. （原始内容存档于2021-01-15）.
^ PyMC forked Aesara to PyTensor. [2023-08-17]. （原始内容存档于2023-07-18）.
^ Hoffman, Matthew D.; Gelman, Andrew. The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research. April 2014, 15: pp. 1593–1623 [2021-01-20]. （原始内容存档于2020-08-11）.
^ Kucukelbir, Alp; Ranganath, Rajesh; Blei, David M. Automatic Variational Inference in Stan 1506 (3431). June 2015. Bibcode:2015arXiv150603431K. arXiv:1506.03431 .

延伸阅读

Probabilistic Programming and Bayesian Methods for Hackers （页面存档备份，存于互联网档案馆）
Computational Statistics in Python （页面存档备份，存于互联网档案馆）

外部链接

PyMC web site （页面存档备份，存于互联网档案馆）
PyMC source （页面存档备份，存于互联网档案馆）, a Git repository hosted on GitHub
Symbolic PyMC （页面存档备份，存于互联网档案馆） is an experimental set of tools that facilitate sophisticated symbolic manipulation of PyMC models

[wikidata-0c221fb585fce7202302f654450566a46ca11249-v3-1] v5.13.1. 2024年4月15日 [2024年4月18日].

[timeline-2] 2.0 ^2.1 PyMC Timeline. PyMC Timeline. [2021-01-20]. （原始内容存档于2018-05-20）.

[3] Salvatier J, Wiecki TV, Fonnesbeck C. (2016) Probabilistic programming in Python using PyMC3. PeerJ Computer Science 2:e55 https://doi.org/10.7717/peerj-cs.55

[Martin2016-4] 4.0 ^4.1 Martin, Osvaldo. Bayesian Analysis with Python. Packt Publishing Ltd. 2016: 31–60 [16 September 2017]. ISBN 9781785889851 （英语）.

[5] Davidson-Pilon, Cameron. Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference. Addison-Wesley Professional. 2015-09-30. ISBN 9780133902921 （英语）.

[6] Hilpisch, Yves. Python for Finance: Analyze Big Financial Data. O'Reilly Media, Inc. 2014-12-11. ISBN 9781491945391 （英语）.

[7] ArviZ — Exploratory analysis of Bayesian models. [2023-09-21]. （原始内容存档于2023-10-11）.

[8] The Algorithms Behind Probabilistic Programming. [2017-03-10]. （原始内容存档于2021-01-29）.

[9] NumFOCUS Announces New Fiscally Sponsored Project: PyMC3. NumFOCUS | Open Code = Better Science. [2017-03-10]. （原始内容存档于2017-09-21）.

[10] Greiner, J.; Burgess, J. M.; Savchenko, V.; Yu, H.-F. On the Fermi-GBM Event 0.4 s after GW150914. The Astrophysical Journal Letters. 2016, 827 (2): L38. Bibcode:2016ApJ...827L..38G. ISSN 2041-8205. arXiv:1606.00314 . doi:10.3847/2041-8205/827/2/L38 （英语）.

[11] Hilbe, Joseph M.; Souza, Rafael S. de; Ishida, Emille E. O. Bayesian Models for Astrophysical Data: Using R, JAGS, Python, and Stan. Cambridge University Press. 2017-04-30 [2021-01-20]. ISBN 9781108210744. （原始内容存档于2021-02-03）（英语）.

[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. Inferring the effectiveness of government interventions against COVID-19. Science. 2020-12-15 [2021-01-20]. doi:10.1126/science.abd9338. （原始内容存档于2021-02-07）.

[13] Systrom, Kevin; Vladek, Thomas; Krieger, Mike. Rt.live Github repository. Rt.live. [10 January 2021]. （原始内容存档于2021-01-06）.

[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. Dose-Dependent Regulation of Alternative Splicing by MBNL Proteins Reveals Biomarkers for Myotonic Dystrophy. PLOS Genetics. 2016-09-28, 12 (9): e1006316. ISSN 1553-7404. PMC 5082313 . PMID 27681373. doi:10.1371/journal.pgen.1006316.

[15] Sharma, Amit; Johansson, Linda; Dunevall, Elin; Wahlgren, Weixiao Y.; Neutze, Richard; Katona, Gergely. Asymmetry in serial femtosecond crystallography data. Acta Crystallographica Section A. 2017-03-01, 73 (2): 93–101. ISSN 2053-2733. PMC 5332129 . PMID 28248658. doi:10.1107/s2053273316018696 （英语）.

[16] Katona, Gergely; Garcia-Bonete, Maria-Jose; Lundholm, Ida. Estimating the difference between structure-factor amplitudes using multivariate Bayesian inference. Acta Crystallographica Section A. 2016-05-01, 72 (3): 406–411. ISSN 2053-2733. PMC 4850660 . PMID 27126118. doi:10.1107/S2053273316003430 （英语）.

[17] Garay, Pablo G.; Martin, Osvaldo A.; Scheraga, Harold A.; Vila, Jorge A. Detection of methylation, acetylation and glycosylation of protein residues by monitoring13C chemical-shift changes: A quantum-chemical study. PeerJ. 2016-07-21, 4: e2253. ISSN 2167-8359. PMC 4963218 . PMID 27547559. doi:10.7717/peerj.2253 （英语）.

[18] Wang, Yan; Huang, Hong; Huang, Lida; Ristic, Branko. Evaluation of Bayesian source estimation methods with Prairie Grass observations and Gaussian plume model: A comparison of likelihood functions and distance measures. Atmospheric Environment. 2017, 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. Age and Growth of An Outbreaking Acanthaster cf. solaris Population within the Great Barrier Reef. Diversity. 2017-03-14, 9 (1): 18. doi:10.3390/d9010018 （英语）.

[20] Tünnermann, Jan; Scharlau, Ingrid. Peripheral Visual Cues: Their Fate in Processing and Effects on Attention and Temporal-Order Perception. Frontiers in Psychology. 2016, 7. ISSN 1664-1078. PMC 5052275 . PMID 27766086. doi:10.3389/fpsyg.2016.01442 （英语）.

[21] Lamblin, Pascal. MILA and the future of Theano. theano-users (邮件列表). 28 September 2017 [28 September 2017]. （原始内容存档于2011-01-22）.

[22] TensorFlow Probability is a library for probabilistic reasoning and statistical analysis. [2022-08-31]. （原始内容存档于2022-09-04）.

[23] Developers, PyMC. Theano, TensorFlow and the Future of PyMC. PyMC Developers. 2018-05-17 [2019-01-25]. （原始内容存档于2020-08-06）.

[24] The Future of PyMC3, or: Theano is Dead, Long Live Theano. PyMC Developers. [10 January 2021]. （原始内容存档于2021-01-15）.

[25] PyMC forked Aesara to PyTensor. [2023-08-17]. （原始内容存档于2023-07-18）.

[NUTS2014-26] Hoffman, Matthew D.; Gelman, Andrew. The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research. April 2014, 15: pp. 1593–1623 [2021-01-20]. （原始内容存档于2020-08-11）.

[kucukelbir20153-27] Kucukelbir, Alp; Ranganath, Rajesh; Blei, David M. Automatic Variational Inference in Stan 1506 (3431). June 2015. Bibcode:2015arXiv150603431K. arXiv:1506.03431 .

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