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贝叶斯网络 (查看源代码)

2021年1月24日 (日) 21:01的版本

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前2个种模式表示的依赖关系是相同的（在给定<math>Y</math> 时，<math>X</math> 和<math>Z</math>是独立的），因此无法区分。然而，第三种模式确实可以被识别的，因为<math>X</math> 和<math>Z</math>是边际独立的，而其他所有变量对都是依赖的。因此，虽然这三个节点的连接方式和前两种模式相同，但这种模式中箭头的方向是部分可识别的。当<math>X</math> 和<math>Z</math>有着共同的父母时，这种不同也能被识别。这个算法已经发展到能系统地确定图的框架，然后由从数据中观察到的条件独立性确定所有箭头的方向。<ref name="pearl2000">{{Cite book | first = Judea | last = Pearl | authorlink = Judea Pearl | title = Causality: Models, Reasoning, and Inference ~~|url={{google books |plainurl=y |id=LLkhAwAAQBAJ}}~~| publisher = [[Cambridge University Press]] | year = 2000 | isbn = 978-0-521-77362-1 | oclc = 42291253 }}</ref><ref>{{cite journal | vauthors = Spirtes P, Glymour C |title=An algorithm for fast recovery of sparse causal graphs |journal=Social Science Computer Review |volume=9 |issue=1 |pages=62–72 |year=1991 |doi=10.1177/089443939100900106 |url=http://repository.cmu.edu/cgi/viewcontent.cgi?article=1316&context=philosophy |format=PDF}}</ref><ref>{{cite book |first1=Peter |last1=Spirtes |first2=Clark N. |last2=Glymour |first3=Richard |last3=Scheines | name-list-format = vanc |title=Causation, Prediction, and Search ~~|url={{google books |plainurl=y |id=VkawQgAACAAJ}}~~ |year=1993 |publisher=Springer-Verlag |isbn=978-0-387-97979-3 |edition=1st}}</ref><ref>{{cite conference |title=Equivalence and synthesis of causal models ~~|url={{google books |plainurl=y |id=ikuuHAAACAAJ}}~~|first1=Thomas |last1=Verma |first2=Judea |last2=Pearl |year=1991 | veditors = Bonissone P, Henrion M, Kanal LN, Lemmer JF | booktitle = UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence |publisher=Elsevier |pages=255–270 |isbn=0-444-89264-8 }}</ref>

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前2个种模式表示的依赖关系是相同的（在给定<math>Y</math> 时，<math>X</math> 和<math>Z</math>是独立的），因此无法区分。然而，第三种模式确实可以被识别的，因为<math>X</math> 和<math>Z</math>是边际独立的，而其他所有变量对都是依赖的。因此，虽然这三个节点的连接方式和前两种模式相同，但这种模式中箭头的方向是部分可识别的。当<math>X</math> 和<math>Z</math>有着共同的父母时，这种不同也能被识别。这个算法已经发展到能系统地确定图的框架，然后由从数据中观察到的条件独立性确定所有箭头的方向。<ref name="pearl2000">{{Cite book | first = Judea | last = Pearl | authorlink = Judea Pearl | title = Causality: Models, Reasoning, and Inference | publisher = [[Cambridge University Press]] | year = 2000 | isbn = 978-0-521-77362-1 | oclc = 42291253 }}</ref><ref>{{cite journal | vauthors = Spirtes P, Glymour C |title=An algorithm for fast recovery of sparse causal graphs |journal=Social Science Computer Review |volume=9 |issue=1 |pages=62–72 |year=1991 |doi=10.1177/089443939100900106 |url=http://repository.cmu.edu/cgi/viewcontent.cgi?article=1316&context=philosophy |format=PDF}}</ref><ref>{{cite book |first1=Peter |last1=Spirtes |first2=Clark N. |last2=Glymour |first3=Richard |last3=Scheines | name-list-format = vanc |title=Causation, Prediction, and Search |year=1993 |publisher=Springer-Verlag |isbn=978-0-387-97979-3 |edition=1st}}</ref><ref>{{cite conference |title=Equivalence and synthesis of causal models|first1=Thomas |last1=Verma |first2=Judea |last2=Pearl |year=1991 | veditors = Bonissone P, Henrion M, Kanal LN, Lemmer JF | booktitle = UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence |publisher=Elsevier |pages=255–270 |isbn=0-444-89264-8 }}</ref>

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===生成一个贝叶斯网络===

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生成一个贝叶斯网络通常从创建一个有向无环图''G''开始，然后使图''G''里的随机变量''X''满足的局部马尔可夫性。有时这个图同时还是一个因果图。接下来，图里的每一个随机变量的概率分布都要被估计出来。在许多情况下，特别是在变量都是离散的情况下，如果 ''X'' 的联合分布是这些单个随机变量的条件分布的乘积，那么 ''X'' 就是 ''G'' 的贝叶斯网络。.<ref>{{cite book |first=Richard E. |last=Neapolitan | name-list-format = vanc |title=Learning Bayesian networks ~~|url={{google books |plainurl=y |id=OlMZAQAAIAAJ}}~~ |year=2004 |publisher=Prentice Hall |isbn=978-0-13-012534-7 }}</ref>

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生成一个贝叶斯网络通常从创建一个有向无环图''G''开始，然后使图''G''里的随机变量''X''满足的局部马尔可夫性。有时这个图同时还是一个因果图。接下来，图里的每一个随机变量的概率分布都要被估计出来。在许多情况下，特别是在变量都是离散的情况下，如果 ''X'' 的联合分布是这些单个随机变量的条件分布的乘积，那么 ''X'' 就是 ''G'' 的贝叶斯网络。.<ref>{{cite book |first=Richard E. |last=Neapolitan | name-list-format = vanc |title=Learning Bayesian networks |year=2004 |publisher=Prentice Hall |isbn=978-0-13-012534-7 }}</ref>

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20世纪80年代后期， Pearl的《智能系统中的概率推理 Probabilistic Reasoning in Intelligent Systems》<ref>{{cite book | vauthors = Pearl J |title=Probabilistic Reasoning in Intelligent Systems |publisher=Morgan Kaufmann |location=San Francisco CA |isbn=978-1558604797 |pages=1988 ~~|url={{google books |plainurl=y |id=AvNID7LyMusC}}~~|date=1988-09-15 }}</ref>和Neapolitan的《专家系统中的概率推理 Probabilistic Reasoning in Expert Systems》<ref>{{cite book |first=Richard E. |last=Neapolitan | title=Probabilistic reasoning in expert systems: theory and algorithms ~~|url={{google books |plainurl=y |id=7X5KLwEACAAJ}}~~ |year=1989 |publisher=Wiley |isbn=978-0-471-61840-9}}</ref> 总结了它们的性质，并将它们确立为一个研究领域。

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20世纪80年代后期， Pearl的《智能系统中的概率推理 Probabilistic Reasoning in Intelligent Systems》<ref>{{cite book | vauthors = Pearl J |title=Probabilistic Reasoning in Intelligent Systems |publisher=Morgan Kaufmann |location=San Francisco CA |isbn=978-1558604797 |pages=1988|date=1988-09-15 }}</ref>和Neapolitan的《专家系统中的概率推理 Probabilistic Reasoning in Expert Systems》<ref>{{cite book |first=Richard E. |last=Neapolitan | title=Probabilistic reasoning in expert systems: theory and algorithms |year=1989 |publisher=Wiley |isbn=978-0-471-61840-9}}</ref> 总结了它们的性质，并将它们确立为一个研究领域。

== 另见 ==

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* {{cite book | last = Darwiche|first=Adnan | name-list-format = vanc |title = Modeling and Reasoning with Bayesian Networks |url=http://www.cambridge.org/9780521884389 |publisher = [[Cambridge University Press]] |year = 2009 |isbn = 978-0521884389}}

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* {{Cite book~~|url={{google books |plainurl=y |id=mPG5RupkTX0C}}~~|title=Philosophy of Statistics|date=2011-05-31|publisher=Elsevier|isbn=9780080930961|language=en|last=Dowe |first=David L. |chapter-url =http://www.csse.monash.edu.au/~dld/Publications/2010/Dowe2010_MML_HandbookPhilSci_Vol7_HandbookPhilStat_MML+hybridBayesianNetworkGraphicalModels+StatisticalConsistency+InvarianceAndUniqueness_pp901-982.pdf |chapter=Hybrid Bayesian network graphical models, statistical consistency, invariance and uniqueness |pp =[http://www.csse.monash.edu.au/~dld/Publications/2010/Dowe2010_MML_HandbookPhilSci_Vol7_HandbookPhilStat_MML+hybridBayesianNetworkGraphicalModels+StatisticalConsistency+InvarianceAndUniqueness_pp901-982.pdf 901–982]}}

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* {{Cite book|title=Philosophy of Statistics|date=2011-05-31|publisher=Elsevier|isbn=9780080930961|language=en|last=Dowe |first=David L. |chapter-url =http://www.csse.monash.edu.au/~dld/Publications/2010/Dowe2010_MML_HandbookPhilSci_Vol7_HandbookPhilStat_MML+hybridBayesianNetworkGraphicalModels+StatisticalConsistency+InvarianceAndUniqueness_pp901-982.pdf |chapter=Hybrid Bayesian network graphical models, statistical consistency, invariance and uniqueness |pp =[http://www.csse.monash.edu.au/~dld/Publications/2010/Dowe2010_MML_HandbookPhilSci_Vol7_HandbookPhilStat_MML+hybridBayesianNetworkGraphicalModels+StatisticalConsistency+InvarianceAndUniqueness_pp901-982.pdf 901–982]}}

* {{cite book | last1 = Fenton | first1 = Norman | last2 = Neil | first2 = Martin E. | name-list-format = vanc | date = November 2007 | chapter-url = http://www.agenarisk.com/resources/apps_bayesian_networks.pdf | chapter = Managing Risk in the Modern World: Applications of Bayesian Networks | title = A Knowledge Transfer Report from the London Mathematical Society and the Knowledge Transfer Network for Industrial Mathematics. | location = [[London|London (England)]] | publisher = [[London Mathematical Society]] }}

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* {{cite news|first=Norman |last=Fenton |first2=Martin E. |last2=Neil | name-list-format = vanc |title=Combining evidence in risk analysis using Bayesian Networks |url=https://www.dcs.qmul.ac.uk/~norman/papers/Combining%20evidence%20in%20risk%20analysis%20using%20BNs.pdf |work=Safety Critical Systems Club Newsletter |volume=13 |issue=4 |location=[[Newcastle upon Tyne]], England |pages=8–13 |date=July 23, 2004 |url-status=dead |archive-url=https://web.archive.org/web/20070927153751/https://www.dcs.qmul.ac.uk/~norman/papers/Combining%20evidence%20in%20risk%20analysis%20using%20BNs.pdf |archive-date=2007-09-27 }}

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* {{cite book | first1 = Andrew | last1 = Gelman | first2 = John B | last2 = Carlin | first3 = Hal S | last3 = Stern | first4 = Donald B | last4 = Rubin | name-list-format = vanc |title=Bayesian Data Analysis |chapter=Part II: Fundamentals of Bayesian Data Analysis: Ch.5 Hierarchical models ~~|chapterurl={{google books |plainurl=y |id=TNYhnkXQSjAC|page=120}}~~ |year=2003 |publisher=[[CRC Press]] |isbn=978-1-58488-388-3 |pages=120– ~~|url={{google books |plainurl=y |id=TNYhnkXQSjAC}}~~}}

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* {{cite book | first1 = Andrew | last1 = Gelman | first2 = John B | last2 = Carlin | first3 = Hal S | last3 = Stern | first4 = Donald B | last4 = Rubin | name-list-format = vanc |title=Bayesian Data Analysis |chapter=Part II: Fundamentals of Bayesian Data Analysis: Ch.5 Hierarchical models |year=2003 |publisher=[[CRC Press]] |isbn=978-1-58488-388-3 |pages=120–}}

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* {{cite book| last = Heckerman | first =David | date = March 1, 1995 | contribution = Tutorial on Learning with Bayesian Networks | contribution-url = http://research.microsoft.com/research/pubs/view.aspx?msr_tr_id=MSR-TR-95-06 | editor-last = Jordan | editor-first = Michael Irwin | title = Learning in Graphical Models | series = Adaptive Computation and Machine Learning | location = [[Cambridge, Massachusetts]] | publication-date = 1998 | publisher = [[MIT Press]] | pages = 301–354 | isbn = 978-0-262-60032-3}}

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* {{cite book| last = Heckerman | first =David | date = March 1, 1995 | contribution = Tutorial on Learning with Bayesian Networks | contribution-url = http://research.microsoft.com/research/pubs/view.aspx?msr_tr_id=MSR-TR-95-06 | editor-last = Jordan | editor-first = Michael Irwin | title = Learning in Graphical Models | series = Adaptive Computation and Machine Learning | location = Cambridge, Massachusetts| publication-date = 1998 | publisher = MIT Press | pages = 301–354 | isbn = 978-0-262-60032-3}}

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:也显示为{{cite journal |date=March 1997|title= Bayesian Networks for Data Mining |journal= [[Data Mining and Knowledge Discovery]]|volume= 1| issue= 1 |pages= 79–119 |doi= 10.1023/A:1009730122752 |last1= Heckerman |first1= David}}

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:也显示为{{cite journal |date=March 1997|title= Bayesian Networks for Data Mining |journal= Data Mining and Knowledge Discovery|volume= 1| issue= 1 |pages= 79–119 |doi= 10.1023/A:1009730122752 |last1= Heckerman |first1= David}}

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早期的版本是[ https://web.archive.org/web/20060719171558/http://Research.Microsoft.com/Research/pubs/view.aspx?msr_tr_id=MSR-TR-95-06技术报告 MSR-TR-95-06] ，微软研究院，1995年3月1日。本文主要研究贝叶斯网络的参数学习和结构学习。

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* {{cite book| last=Jensen |first=Finn V| last2=Nielsen | first2 = Thomas D. | name-list-format = vanc | title = Bayesian Networks and Decision Graphs~~|url={{google books |plainurl=y |id=cWLaBwAAQBAJ}}~~|edition=2nd |series=Information Science and Statistics series | publisher = [[Springer Science+Business Media|Springer-Verlag]] |location=[[New York City|New York]] | date = June 6, 2007| isbn=978-0-387-68281-5}}

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* {{cite book| last=Jensen |first=Finn V| last2=Nielsen | first2 = Thomas D. | name-list-format = vanc | title = Bayesian Networks and Decision Graphs|edition=2nd |series=Information Science and Statistics series | publisher = [[Springer Science+Business Media|Springer-Verlag]] |location=[[New York City|New York]] | date = June 6, 2007| isbn=978-0-387-68281-5}}

* {{cite journal| last=Karimi |first=Kamran| last2=Hamilton | first2 = Howard J. | name-list-format = vanc | title = Finding temporal relations: Causal bayesian networks vs. C4. 5| journal = Twelfth International Symposium on Methodologies for Intelligent Systems | date = 2000 | url = http://www.kamran-karimi.com/pubs/khISMIS2000.pdf}}

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* {{cite book| last=Korb| first=Kevin B.|last2 = Nicholson|first2 = Ann E. | name-list-format = vanc | title = Bayesian Artificial Intelligence~~|url={{google books |plainurl=y |id=LxXOBQAAQBAJ}}~~ | edition = 2nd | publisher = [[Chapman & Hall]] ([[CRC Press]]) | date = December 2010 | isbn = 978-1-58488-387-6 | series=CRC Computer Science & Data Analysis | doi=10.1007/s10044-004-0214-5}}

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* {{cite book| last=Korb| first=Kevin B.|last2 = Nicholson|first2 = Ann E. | name-list-format = vanc | title = Bayesian Artificial Intelligence| edition = 2nd | publisher = [[Chapman & Hall]] ([[CRC Press]]) | date = December 2010 | isbn = 978-1-58488-387-6 | series=CRC Computer Science & Data Analysis | doi=10.1007/s10044-004-0214-5}}

* {{cite journal | vauthors = Lunn D, Spiegelhalter D, Thomas A, Best N | title = The BUGS project: Evolution, critique and future directions | journal = Statistics in Medicine | volume = 28 | issue = 25 | pages = 3049–67 | date = November 2009 | pmid = 19630097 | doi = 10.1002/sim.3680 }}

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* {{cite journal |last= Pearl|first= Judea |authorlink= Judea Pearl | name-list-format = vanc |date=September 1986|title= Fusion, propagation, and structuring in belief networks |journal= [[Artificial Intelligence (journal)|Artificial Intelligence]]|volume= 29 |issue= 3 |pages= 241–288 |doi= 10.1016/0004-3702(86)90072-X}}

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* {{cite book | last = Pearl|first=Judea| name-list-format = vanc |authorlink = Judea Pearl |title = Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference~~|url={{google books |plainurl=y |id=mn2jBQAAQBAJ}}~~ |edition = 2nd printing|publisher = [[Morgan Kaufmann]] |location= [[San Francisco, California]] |year = 1988 |isbn = 978-0-934613-73-6 | series=Representation and Reasoning Series}}

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* {{cite book | last = Pearl|first=Judea| name-list-format = vanc |authorlink = Judea Pearl |title = Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference|edition = 2nd printing|publisher = [[Morgan Kaufmann]] |location= [[San Francisco, California]] |year = 1988 |isbn = 978-0-934613-73-6 | series=Representation and Reasoning Series}}

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* {{cite book|last=Pearl|first=Judea|authorlink=Judea Pearl |last2=Russell |first2=Stuart |authorlink2=Stuart J. Russell |contribution=Bayesian Networks |editor-last=Arbib |editor-first=Michael A.| name-list-format = vanc |editor-link=Michael A. Arbib |title=Handbook of Brain Theory and Neural Networks~~|url={{google books |plainurl=y |id=Av6qWhtw0-EC}}~~ |pages=157–160 |location=[[Cambridge, Massachusetts]]|date=November 2002| publisher = Bradford Books ([[MIT Press]]) | isbn=978-0-262-01197-6}}

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* {{cite book|last=Pearl|first=Judea|authorlink=Judea Pearl |last2=Russell |first2=Stuart |authorlink2=Stuart J. Russell |contribution=Bayesian Networks |editor-last=Arbib |editor-first=Michael A.| name-list-format = vanc |editor-link=Michael A. Arbib |title=Handbook of Brain Theory and Neural Networks|pages=157–160 |location=[[Cambridge, Massachusetts]]|date=November 2002| publisher = Bradford Books ([[MIT Press]]) | isbn=978-0-262-01197-6}}

* {{Russell Norvig 2003}}.

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==延伸阅读==

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* {{cite book | title = Bayesian Networks and BayesiaLab – A practical introduction for researchers~~|url={{google books |plainurl=y |id=etXXsgEACAAJ}}~~ | first1 = Stefan | last1 = Conrady | first2 = Lionel | last2 = Jouffe | name-list-format = vanc | isbn = 978-0-9965333-0-0 | publisher = Bayesian USA | location = Franklin, Tennessee |date=2015-07-01 }}

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* {{cite book | title = Bayesian Networks and BayesiaLab – A practical introduction for researchers|first1 = Stefan | last1 = Conrady | first2 = Lionel | last2 = Jouffe | name-list-format = vanc | isbn = 978-0-9965333-0-0 | publisher = Bayesian USA | location = Franklin, Tennessee |date=2015-07-01 }}

* {{cite web | url = http://pages.cs.wisc.edu/~dyer/cs540/handouts/charniak.pdf | title = Bayesian networks without tears | first = Eugene | last = Charniak | name-list-format = vanc | work = AI Magazine | date = Winter 1991 }}

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* {{cite book | first1 =Rudolf | last1 = Kruse | first2 = Christian | last2 = Borgelt | first3 = Frank | last3 = Klawonn | first4 = Christian | last4 = Moewes | first5 = Matthias | last5 = Steinbrecher | first6 = Pascal | last6 = Held | name-list-format = vanc | title = Computational Intelligence A Methodological Introduction ~~|url={{google books |plainurl=y |id=etXXsgEACAAJ}}~~| date=2013 |publisher = Springer-Verlag | location = London | isbn = 978-1-4471-5012-1 }}

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* {{cite book | first1 =Rudolf | last1 = Kruse | first2 = Christian | last2 = Borgelt | first3 = Frank | last3 = Klawonn | first4 = Christian | last4 = Moewes | first5 = Matthias | last5 = Steinbrecher | first6 = Pascal | last6 = Held | name-list-format = vanc | title = Computational Intelligence A Methodological Introduction | date=2013 |publisher = Springer-Verlag | location = London | isbn = 978-1-4471-5012-1 }}

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* {{cite book | first1 = Christian | last1 = Borgelt | first2 = Matthias | last2 = Steinbrecher | first3 = Rudolf | last3 = Kruse | name-list-format = vanc | title = Graphical Models – Representations for Learning, Reasoning and Data Mining ~~|url={{google books |plainurl=y |id=I8Fa-LKDpF0C}}~~ | date = 2009 | publisher = Wiley | location = Chichester | isbn = 978-0-470-74956-2 | edition = Second }}

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* {{cite book | first1 = Christian | last1 = Borgelt | first2 = Matthias | last2 = Steinbrecher | first3 = Rudolf | last3 = Kruse | name-list-format = vanc | title = Graphical Models – Representations for Learning, Reasoning and Data Mining |date = 2009 | publisher = Wiley | location = Chichester | isbn = 978-0-470-74956-2 | edition = Second }}

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