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Independence for Full Conditional Measures, Graphoids and Bayesian Networks

Summary: Independence for Full Conditional Measures, Graphoids and
Bayesian Networks
Fabio G. Cozman
Universidade de Sao Paulo
Teddy Seidenfeld
Carnegie Mellon University
February 28, 2007
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 con-
ditioning 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, char-
acterize the form of a full conditional measure under full independence, and suggest how to
build a theory of Bayesian networks that accommodates null events.
1 Introduction
In this paper we wish to consider independence concepts associated with full conditional measures
[25]. That is, we wish to allow conditioning to be a primitive notion, defined even on null events
(events of zero probability). The advantages of a probability theory that takes conditioning as a
primitive have been explored by many authors, such as de Finetti [22] and his followers [11, 17],


Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University


Collections: Mathematics