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About: Conditional Independence, Given a Random Vector

Module by: Paul E Pfeiffer. E-mail the author

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Name: Conditional Independence, Given a Random Vector
ID: m23813
Language: English (en)
Summary: The notion of conditional independence is extended to random variables by considering appropriate indicator functions, then extending to more general random vectors. A variety of equivalent conditions provide a basis for practical analysis and interpretation. An important application is the Bayesian approach to statistics. The essential idea is that an unknown parameter about which there is uncertainty is modeled as the value of a random variable. The name Bayesian comes from the role of Bayesian reversal in the analysis. The Bayesian estimate often seems preferable for small samples, and it has the advantage that prior information may be utilized. The sampling procedure upgrades the prior distribution.
Subject: Mathematics and Statistics
Keywords: Bayesian reversal, Bayesian statistics, Concept, Equivalences, Interpretation: mean-square estimator
License: Creative Commons Attribution License CC-BY 3.0

Authors: Paul E Pfeiffer (perhp@earthlink.net)
Copyright Holders: Paul E Pfeiffer (perhp@earthlink.net)
Maintainers: Paul E Pfeiffer (perhp@earthlink.net), Daniel Williamson (dcwill@cnx.org), C. Sidney Burrus (csb@rice.edu)

Latest version: 1.6 (history)
First publication date: Apr 20, 2009 12:11 pm -0500
Last revision to module: Sep 18, 2009 12:07 pm -0500

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XML: m23813_1.6.cnxml XML that defines the structure and contents of the module, minus any included media files. Can be reimported in the editing interface. Learn more.

Version History

Version: 1.6 Sep 18, 2009 12:07 pm -0500 by Daniel Williamson
Changes:
added google analytics tracking code

Version: 1.5 Jul 27, 2009 11:43 am -0500 by Daniel Williamson
Changes:
disjoint union fix

Version: 1.4 Jun 19, 2009 11:00 am -0500 by Daniel Williamson
Changes:
m-file fixes, supplemental links, metadata updated

Version: 1.3 Jun 9, 2009 5:01 pm -0500 by Daniel Williamson
Changes:
updated links, images, and accessibility

Version: 1.2 May 26, 2009 4:16 pm -0500 by Daniel Williamson
Changes:
fixed module names, and updated content structure

Version: 1.1 May 23, 2009 10:20 am -0500 by Paul E Pfeiffer
Changes:
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Pfeiffer P. Conditional Independence, Given a Random Vector [OpenStax-CNX Web site]. September 18, 2009. Available at: http://cnx.org/content/m23813/1.6/.

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Pfeiffer, P. (2009, September 18). Conditional Independence, Given a Random Vector. Retrieved from the OpenStax-CNX Web site: http://cnx.org/content/m23813/1.6/

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Pfeiffer, Paul. "Conditional Independence, Given a Random Vector." OpenStax-CNX. September 18, 2009. http://cnx.org/content/m23813/1.6/.

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Paul Pfeiffer, "Conditional Independence, Given a Random Vector," OpenStax-CNX, September 18, 2009, http://cnx.org/content/m23813/1.6/.

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Pfeiffer, P. 2009. Conditional Independence, Given a Random Vector. OpenStax-CNX, September 18, 2009. http://cnx.org/content/m23813/1.6/.

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Pfeiffer, Paul. Conditional Independence, Given a Random Vector. OpenStax-CNX. 18 Sep. 2009 <http://cnx.org/content/m23813/1.6/>.