PyMC

**PyMC**
原作者	PyMC開發團隊
首次發佈	2013年5月4日
當前版本	5.15.0 (2024年5月13日；穩定版本);
原始碼庫	https://github.com/pymc-devs/pymc
程式語言	Python
作業系統	類Unix, Mac OS X, Microsoft Windows
平台	Intel x86 – 32-bit, x64
類型	統計包（英語：List of statistical software）
許可協議	Apache License, Version 2.0
網站	www.pymc.io

PyMC（曾叫做PyMC3^[2]）是一個Python包，用於貝葉斯統計建模和概率機器學習，它聚焦於高級馬爾可夫鏈蒙特卡洛法和變分擬合算法^[3]^[4]^[5]。

概述

PyMC曾經叫做PyMC3，不同於早先的使用Fortran擴展進行計算的PyMC2，它依靠Theano來進行自動微分、計算優化和動態C語言編譯^[4]^[6]。從版本3.8開始PyMC依據ArviZ（英語：ArviZ）來進行數據可視化和貝葉斯推斷的探索分析（英語：Exploratory data analysis）^[7]。PyMC和Stan（英語：Stan (software)）是兩個最流行的概率編程工具^[8]。

PyMC是開源項目，由社區開發並在財務上得到NumFocus贊助^[9]。PyMC已經在很多領域中被用於解決推斷問題，包括天文學^[10]^[11]、流行病學^[12]^[13]、分子生物學^[14]、晶體學^[15]^[16]、化學^[17]、生態學^[18]^[19]和心理學^[20]。

在Theano於2017年宣佈計劃停止開發之後^[21]，PyMC團隊曾評估採用TensorFlow Probability^[22]作為計算後端^[23]，但是在2020年接管Theano的開發^[24]。在2021年1月絕大部份的Theano代碼基被重新建造，並增加了通過JAX和Numba的編譯，修訂後的這個計算後端以新名字Aesara發行。PyMC團隊在2021年6月將PyMC3更名為PyMC^[2]。2022年11月28日，PyMC團隊宣佈採用從Aesara計劃分叉出PyTensor^[25]。

推論引擎

PyMC實現了不基於梯度的和基於梯度的馬爾可夫鏈蒙特卡洛（MCMC）算法用於貝葉斯推斷和隨機（Stochastic（英語：Stochastic）），基於梯度的變分貝葉斯方法（英語：variational Bayesian methods）用於近似貝葉斯推斷。

MCMC算法：
- No-U-Turn採樣（NUTS）^[26]，是哈密頓蒙特卡洛（英語：Hamiltonian Monte Carlo）的變體和PyMC3用於連續變量的缺省引擎。
- 梅特羅波利斯-黑斯廷斯算法，是PyMC3用於離散變量的缺省引擎。
- 順序蒙特卡洛算法。
變分推斷算法：
- 黑箱變分推斷^[27]。

參見

Stan（英語：Stan (software)）是用C++編寫統計推論的概率程式語言。

引用

^ v5.15.0. 2024年5月13日 [2024年5月15日].
^ ^2.0 ^2.1 PyMC Timeline. PyMC Timeline. [2021-01-20]. （原始內容存檔於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 （英語）.
^ Davidson-Pilon, Cameron. Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference. Addison-Wesley Professional. 2015-09-30. ISBN 9780133902921 （英語）.
^ Hilpisch, Yves. Python for Finance: Analyze Big Financial Data. O'Reilly Media, Inc. 2014-12-11. ISBN 9781491945391 （英語）.
^ ArviZ — Exploratory analysis of Bayesian models. [2023-09-21]. （原始內容存檔於2023-10-11）.
^ The Algorithms Behind Probabilistic Programming. [2017-03-10]. （原始內容存檔於2021-01-29）.
^ NumFOCUS Announces New Fiscally Sponsored Project: PyMC3. NumFOCUS | Open Code = Better Science. [2017-03-10]. （原始內容存檔於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 （英語）.
^ 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. （原始內容存檔於2021-02-03）（英語）.
^ 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. （原始內容存檔於2021-02-07）.
^ Systrom, Kevin; Vladek, Thomas; Krieger, Mike. Rt.live Github repository. Rt.live. [10 January 2021]. （原始內容存檔於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 （英語）.
^ 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 （英語）.
^ 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 （英語）.
^ 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 （英語）.
^ 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 （英語）.
^ Lamblin, Pascal. MILA and the future of Theano. theano-users (郵件列表). 28 September 2017 [28 September 2017]. （原始內容存檔於2011-01-22）.
^ TensorFlow Probability is a library for probabilistic reasoning and statistical analysis. [2022-08-31]. （原始內容存檔於2022-09-04）.
^ Developers, PyMC. Theano, TensorFlow and the Future of PyMC. PyMC Developers. 2018-05-17 [2019-01-25]. （原始內容存檔於2020-08-06）.
^ The Future of PyMC3, or: Theano is Dead, Long Live Theano. PyMC Developers. [10 January 2021]. （原始內容存檔於2021-01-15）.
^ PyMC forked Aesara to PyTensor. [2023-08-17]. （原始內容存檔於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]. （原始內容存檔於2020-08-11）.
^ Kucukelbir, Alp; Ranganath, Rajesh; Blei, David M. Automatic Variational Inference in Stan 1506 (3431). June 2015. Bibcode:2015arXiv150603431K. arXiv:1506.03431 .

延伸閱讀

Probabilistic Programming and Bayesian Methods for Hackers （頁面存檔備份，存於互聯網檔案館）
Computational Statistics in Python （頁面存檔備份，存於互聯網檔案館）

外部連結

PyMC web site （頁面存檔備份，存於互聯網檔案館）
PyMC source （頁面存檔備份，存於互聯網檔案館）, a Git repository hosted on GitHub
Symbolic PyMC （頁面存檔備份，存於互聯網檔案館） is an experimental set of tools that facilitate sophisticated symbolic manipulation of PyMC models

[wikidata-4306588744b13df5764ff779852408a5e855087e-v3-1] v5.15.0. 2024年5月13日 [2024年5月15日].

[timeline-2] 2.0 ^2.1 PyMC Timeline. PyMC Timeline. [2021-01-20]. （原始內容存檔於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 （英語）.

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

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

[7] ArviZ — Exploratory analysis of Bayesian models. [2023-09-21]. （原始內容存檔於2023-10-11）.

[8] The Algorithms Behind Probabilistic Programming. [2017-03-10]. （原始內容存檔於2021-01-29）.

[9] NumFOCUS Announces New Fiscally Sponsored Project: PyMC3. NumFOCUS | Open Code = Better Science. [2017-03-10]. （原始內容存檔於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 （英語）.

[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. （原始內容存檔於2021-02-03）（英語）.

[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. （原始內容存檔於2021-02-07）.

[13] Systrom, Kevin; Vladek, Thomas; Krieger, Mike. Rt.live Github repository. Rt.live. [10 January 2021]. （原始內容存檔於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 （英語）.

[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 （英語）.

[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 （英語）.

[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 （英語）.

[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 （英語）.

[21] Lamblin, Pascal. MILA and the future of Theano. theano-users (郵件列表). 28 September 2017 [28 September 2017]. （原始內容存檔於2011-01-22）.

[22] TensorFlow Probability is a library for probabilistic reasoning and statistical analysis. [2022-08-31]. （原始內容存檔於2022-09-04）.

[23] Developers, PyMC. Theano, TensorFlow and the Future of PyMC. PyMC Developers. 2018-05-17 [2019-01-25]. （原始內容存檔於2020-08-06）.

[24] The Future of PyMC3, or: Theano is Dead, Long Live Theano. PyMC Developers. [10 January 2021]. （原始內容存檔於2021-01-15）.

[25] PyMC forked Aesara to PyTensor. [2023-08-17]. （原始內容存檔於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]. （原始內容存檔於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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