A.P. Dawid, Conditional Independence, In Encyclopedia of Statistical Science (Update) Vol 3, Wiley, New York, 1999. Home/Search Document Details and Download
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Independence Concepts for Belief Functions - Yaghlane, Smets (2000) (Correct)
....A. The commonality function q(A) is useful for simplifying some computations. It is proved that m, bel, pl and q are in one toone correspondence with each other [14] 3 4 Belief Function Independence The notion of informational irrelevance has been extensively studied in probability theory [6] [7], 12] 13] where it is identified with independence or more specifically conditional independence. The concept of independence has also been studied in non probabilistic frameworks such that Spohn s theory of ordinal conditional functions [17] Zadeh s possibility theory [1] 3] 8] 9] ....
....#X (x)P XY #Y (y) where P XY #X and P XY #Y are the marginal probabilities of P on X and Y , respectively . P XY [y] #X (x) P XY #X (x) where P XY [y] #X is the conditional probability on X given y. Remark. This notation is more cumbersome than the usual one (i.e. such as in [7], 13] but it helps when belief functions are involved as it avoids confusion. The first definition of independence is presented in terms of the factorization of the joint probability distribution through its marginal distributions on X and Y , respectively (a mathematical property) However, ....
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A. P. Dawid, Conditional Independence, In Encyclopedia of Statistical Science (Update) Volume 3, Wiley, New York, 1999.
Belief Function Independence: I. The Marginal Case. - Yaghlane, Smets, Mellouli (2000) (Correct)
....[16] # Address correspondence to Boutheina Ben Yaghlane, AMID, Universite de Tunis, IHECCarthage Presidence 2016 Tunis, Tunisia. E mail: boutheina.yaghlane ihec.rnu.tn and psmets ulb.ac. be 1 The notion of informational irrelevance has been extensively studied in probability theory [7] [8], 15] 16] where it is identified with independence. The concept of independence has also been studied in other non probabilistic frameworks such that Spohn s theory of ordinal conditional functions [22] Zadeh s possibility theory [1] 4] 9] 11] 24] 27] upper and lower probabilities ....
....[y] #X (x) P XY #X (x) where P XY [y] #X is the conditional probability on X given y. In fact, thanks to the additivity of probability measures, it is su#cient that the property holds for all x i # X, y j # Y . Remark. Our notation is more cumbersome than the usual one (i.e. such as in [8], 16] but it helps when belief functions are involved as it avoids confusion. The first definition of independence is presented in terms of the factorization of the joint probability distribution through its marginal distributions on X and Y , respectively (a mathematical property) It is ....
[Article contains additional citation context not shown here]
A.P. Dawid, Conditional Independence, In Encyclopedia of Statistical Science (Update) Volume 3, Wiley, New York, 1999.
On Conditional Belief Function Independence - BenYaghlane, Smets, Mellouli (Correct)
....2 K. Mellouli 1 1 AMID, University of Tunisia boutheina.yaghlane, khaled.mellouli ihec.rnu.tn 2 IRIDIA, Universite Libre de Bruxelles psmets ulb.ac.be Extended Abstract. The concept of conditional independence has been extensively studied in probability theory (see, for instance, 2] [3], 6] Pearl and Paz [7] have introduced some basic properties of the conditional independence relation, called graphoid axioms . These axioms are satisfied not only by probabilistic conditional independence, but also by embedded multi valued dependency models in relational databases [8] ....
....is to propose the new definitions of conditional independence when uncertainty is expressed under the form of belief functions and then to discuss the relationships between these definitions. The notion of conditional independence is given with the conditional independence relations [6] 2] [3], which successfully depict our intuition about how dependencies should update in response to new pieces of information. This paper is organized as follows: we first recall the definition of probabilistic conditional independence. Then, after extending the definition of evidential and cognitive ....
A.P. Dawid, Conditional Independence, In Encyclopedia of Statistical Science (Update) Volume 3, Wiley, New York, 1999.
Conditional Independence For Statistics And AI - Dawid (1997) Self-citation (Dawid) (Correct)
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Dawid, A. P. (1997). Conditional independence. Encyclopedia of Statistical Science (Update). Wiley-Interscience (to appear). An overview of many of the ideas presented here.
On the Flexibility of Theoretical Models - For Pattern Recognition (Correct)
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A.P. Dawid, Conditional Independence, In Encyclopedia of Statistical Science (Update) Vol 3, Wiley, New York, 1999.
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