A Note of Caution on Maximizing Entropy

The Principle of Maximum Entropy is often used to update probabilities due to evidence instead of performing Bayesian updating using Bayes’ Theorem, and its use often has efficacious results. However, in some circumstances the results seem unacceptable and unintuitive. This paper discusses some of t...
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Autor*in:	Richard E. Neapolitan [verfasserIn] Xia Jiang [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2014

Schlagwörter:	maximum entropy classical approach limiting frequency Bayesian subjective probability

Übergeordnetes Werk:	In: Entropy - MDPI AG, 2003, 16(2014), 7, Seite 4004-4014
Übergeordnetes Werk:	volume:16 ; year:2014 ; number:7 ; pages:4004-4014

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DOI / URN:	10.3390/e16074004

Katalog-ID:	DOAJ022828583

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allfieldsGer	10.3390/e16074004 doi (DE-627)DOAJ022828583 (DE-599)DOAJ8f750b698554402baf9bb42bf1b92053 DE-627 ger DE-627 rakwb eng QB460-466 QC1-999 Richard E. Neapolitan verfasserin aut A Note of Caution on Maximizing Entropy 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The Principle of Maximum Entropy is often used to update probabilities due to evidence instead of performing Bayesian updating using Bayes’ Theorem, and its use often has efficacious results. However, in some circumstances the results seem unacceptable and unintuitive. This paper discusses some of these cases, and discusses how to identify some of the situations in which this principle should not be used. The paper starts by reviewing three approaches to probability, namely the classical approach, the limiting frequency approach, and the Bayesian approach. It then introduces maximum entropy and shows its relationship to the three approaches. Next, through examples, it shows that maximizing entropy sometimes can stand in direct opposition to Bayesian updating based on reasonable prior beliefs. The paper concludes that if we take the Bayesian approach that probability is about reasonable belief based on all available information, then we can resolve the conflict between the maximum entropy approach and the Bayesian approach that is demonstrated in the examples. maximum entropy classical approach limiting frequency Bayesian subjective probability Science Q Astrophysics Physics Xia Jiang verfasserin aut In Entropy MDPI AG, 2003 16(2014), 7, Seite 4004-4014 (DE-627)316340359 (DE-600)2014734-X 10994300 nnns volume:16 year:2014 number:7 pages:4004-4014 https://doi.org/10.3390/e16074004 kostenfrei https://doaj.org/article/8f750b698554402baf9bb42bf1b92053 kostenfrei http://www.mdpi.com/1099-4300/16/7/4004 kostenfrei https://doaj.org/toc/1099-4300 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 16 2014 7 4004-4014
allfieldsSound	10.3390/e16074004 doi (DE-627)DOAJ022828583 (DE-599)DOAJ8f750b698554402baf9bb42bf1b92053 DE-627 ger DE-627 rakwb eng QB460-466 QC1-999 Richard E. Neapolitan verfasserin aut A Note of Caution on Maximizing Entropy 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The Principle of Maximum Entropy is often used to update probabilities due to evidence instead of performing Bayesian updating using Bayes’ Theorem, and its use often has efficacious results. However, in some circumstances the results seem unacceptable and unintuitive. This paper discusses some of these cases, and discusses how to identify some of the situations in which this principle should not be used. The paper starts by reviewing three approaches to probability, namely the classical approach, the limiting frequency approach, and the Bayesian approach. It then introduces maximum entropy and shows its relationship to the three approaches. Next, through examples, it shows that maximizing entropy sometimes can stand in direct opposition to Bayesian updating based on reasonable prior beliefs. The paper concludes that if we take the Bayesian approach that probability is about reasonable belief based on all available information, then we can resolve the conflict between the maximum entropy approach and the Bayesian approach that is demonstrated in the examples. maximum entropy classical approach limiting frequency Bayesian subjective probability Science Q Astrophysics Physics Xia Jiang verfasserin aut In Entropy MDPI AG, 2003 16(2014), 7, Seite 4004-4014 (DE-627)316340359 (DE-600)2014734-X 10994300 nnns volume:16 year:2014 number:7 pages:4004-4014 https://doi.org/10.3390/e16074004 kostenfrei https://doaj.org/article/8f750b698554402baf9bb42bf1b92053 kostenfrei http://www.mdpi.com/1099-4300/16/7/4004 kostenfrei https://doaj.org/toc/1099-4300 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 16 2014 7 4004-4014
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source	In Entropy 16(2014), 7, Seite 4004-4014 volume:16 year:2014 number:7 pages:4004-4014
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author	Richard E. Neapolitan
spellingShingle	Richard E. Neapolitan misc QB460-466 misc QC1-999 misc maximum entropy misc classical approach misc limiting frequency misc Bayesian misc subjective probability misc Science misc Q misc Astrophysics misc Physics A Note of Caution on Maximizing Entropy
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topic_title	QB460-466 QC1-999 A Note of Caution on Maximizing Entropy maximum entropy classical approach limiting frequency Bayesian subjective probability
topic	misc QB460-466 misc QC1-999 misc maximum entropy misc classical approach misc limiting frequency misc Bayesian misc subjective probability misc Science misc Q misc Astrophysics misc Physics
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abstract	The Principle of Maximum Entropy is often used to update probabilities due to evidence instead of performing Bayesian updating using Bayes’ Theorem, and its use often has efficacious results. However, in some circumstances the results seem unacceptable and unintuitive. This paper discusses some of these cases, and discusses how to identify some of the situations in which this principle should not be used. The paper starts by reviewing three approaches to probability, namely the classical approach, the limiting frequency approach, and the Bayesian approach. It then introduces maximum entropy and shows its relationship to the three approaches. Next, through examples, it shows that maximizing entropy sometimes can stand in direct opposition to Bayesian updating based on reasonable prior beliefs. The paper concludes that if we take the Bayesian approach that probability is about reasonable belief based on all available information, then we can resolve the conflict between the maximum entropy approach and the Bayesian approach that is demonstrated in the examples.
abstractGer	The Principle of Maximum Entropy is often used to update probabilities due to evidence instead of performing Bayesian updating using Bayes’ Theorem, and its use often has efficacious results. However, in some circumstances the results seem unacceptable and unintuitive. This paper discusses some of these cases, and discusses how to identify some of the situations in which this principle should not be used. The paper starts by reviewing three approaches to probability, namely the classical approach, the limiting frequency approach, and the Bayesian approach. It then introduces maximum entropy and shows its relationship to the three approaches. Next, through examples, it shows that maximizing entropy sometimes can stand in direct opposition to Bayesian updating based on reasonable prior beliefs. The paper concludes that if we take the Bayesian approach that probability is about reasonable belief based on all available information, then we can resolve the conflict between the maximum entropy approach and the Bayesian approach that is demonstrated in the examples.
abstract_unstemmed	The Principle of Maximum Entropy is often used to update probabilities due to evidence instead of performing Bayesian updating using Bayes’ Theorem, and its use often has efficacious results. However, in some circumstances the results seem unacceptable and unintuitive. This paper discusses some of these cases, and discusses how to identify some of the situations in which this principle should not be used. The paper starts by reviewing three approaches to probability, namely the classical approach, the limiting frequency approach, and the Bayesian approach. It then introduces maximum entropy and shows its relationship to the three approaches. Next, through examples, it shows that maximizing entropy sometimes can stand in direct opposition to Bayesian updating based on reasonable prior beliefs. The paper concludes that if we take the Bayesian approach that probability is about reasonable belief based on all available information, then we can resolve the conflict between the maximum entropy approach and the Bayesian approach that is demonstrated in the examples.
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