## Independence for Full Conditional Measures, Graphoids and Bayesian Networks (2007)

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### BibTeX

@MISC{Cozman07independencefor,

author = {Fabio G. Cozman and Teddy Seidenfeld},

title = { Independence for Full Conditional Measures, Graphoids and Bayesian Networks},

year = {2007}

}

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### Abstract

This paper examines definitions of independence for events and variables in the context of full conditional measures; that is, when conditional probability is a primitive notion and conditioning is allowed on null events. Several independence concepts are evaluated with respect to graphoid properties; we show that properties of weak union, contraction and intersection may fail when null events are present. We propose a concept of “full” independence, characterize the form of a full conditional measure under full independence, and suggest how to build a theory of Bayesian networks that accommodates null events.