Conditional Independence in Applied Probability

P. E. Pfeiffer

ISBN 10: 1461263379 / ISBN 13: 9781461263371

Verlag: Birkhäuser Boston, Birkhäuser Boston Nov 2011, 2011

Beschreibung

This item is printed on demand - Print on Demand Titel. Neuware -It would be difficult to overestimate the importance of stochastic independence in both the theoretical development and the practical appli cations of mathematical probability. The concept is grounded in the idea that one event does not 'condition' another, in the sense that occurrence of one does not affect the likelihood of the occurrence of the other. This leads to a formulation of the independence condition in terms of a simple 'product rule,' which is amazingly successful in capturing the essential ideas of independence. However, there are many patterns of 'conditioning' encountered in practice which give rise to quasi independence conditions. Explicit and precise incorporation of these into the theory is needed in order to make the most effective use of probability as a model for behavioral and physical systems. We examine two concepts of conditional independence. The first concept is quite simple, utilizing very elementary aspects of probability theory. Only algebraic operations are required to obtain quite important and useful new results, and to clear up many ambiguities and obscurities in the literature.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 168 pp. Englisch.

Bestandsnummer des Verkäufers 9781461263371

Bibliografische Details

• Titel: Conditional Independence in Applied Probability
• Verlag: Birkhäuser Boston, Birkhäuser Boston Nov 2011
• Erscheinungsjahr: 2011
• Sprache: Englisch
• ISBN-10: 1461263379
• ISBN-13: 9781461263371
• Einband: Taschenbuch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

It would be difficult to overestimate the importance of stochastic independence in both the theoretical development and the practical appli­ cations of mathematical probability. The concept is grounded in the idea that one event does not "condition" another, in the sense that occurrence of one does not affect the likelihood of the occurrence of the other. This leads to a formulation of the independence condition in terms of a simple "product rule," which is amazingly successful in capturing the essential ideas of independence. However, there are many patterns of "conditioning" encountered in practice which give rise to quasi independence conditions. Explicit and precise incorporation of these into the theory is needed in order to make the most effective use of probability as a model for behavioral and physical systems. We examine two concepts of conditional independence. The first concept is quite simple, utilizing very elementary aspects of probability theory. Only algebraic operations are required to obtain quite important and useful new results, and to clear up many ambiguities and obscurities in the literature.