Dawid, A.P. (1980). Conditional independence for statistical operations. The Annals of Statistics 8, 598-617.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....between pairs or even subsets of variables. These independences are represented by missing edges in a graph which consists of vertices depicting the variables 1 and edges depicting associations between them. An association has to be understood as the absence of a conditional independence (Dawid, 1979, 1980). So called Markov properties describe the conditions which have to be ful lled by the distribution model to connect the graph with these independence statements (Frydenberg, 1990, Lauritzen, 1996) Distributions which are able to capture these demands are the multinomial, multivariate normal, and ....

Dawid, A.P. (1980). Conditional independence for statistical operations. The Annals of Statistics 8, 598-617.

.... of pairwise, local, and global Markov properties is required when concluding from properties of the graph, like separation of two sets of vertices A and B by a third set C, to those of the joint distribution, like the conditional independence of XA and XB given X C brie y written as A B j C (Dawid, 1979, 1980). That means, missing edges in the underlying graph can be correctly interpreted as conditional independences. The conditions for marginalization, collapsibility, and decomposition of the ML estimation for graphical models with CG distribution can be found in Frydenberg (1990) and Frydenberg and ....

Dawid, A.P. (1980). Conditional independence for statistical operations. The Annals of Statistics 8, 598-617.

....conditional independence plays an important role for the persued factorization. In the following, this property is de ned similarly to Dawid (1979) by means of a factorization formula for the joint density and for the joint cdf. A more theoretical de nition via versions of conditional expectations (Dawid, 1980) is possible but not necessary in this context. Here, the de nition close to density functions and cdf s makes the connection to the factorization of these functions obvious. For disjoint subsets A; B, and C of V XA and XB are said to be (i) conditionally independent given X C = x C if the ....

....jx C ) 1.3) or FA[BjC (x A ; xB jx C ) FAjC (x A jx C )FBjC (x B jx C ) 1.4) ii) conditionally independent given X C if XA and XB are conditionally independent given X C = x C for all x C 2 IR jCj . Then we write XA XB j X C or brie y A B j C. The notation A B j C was introduced by Dawid (1979, 1980). He discusses basic properties, applications, and possible interpretations of the concept of conditional independence in detail. His ideas are not only of theoretical interest. They are, for instance, recovered in the theory of graphical models. For convenience, let us recall the basic ideas of ....

Dawid, A.P. (1980). Conditional independence for statistical operations. The Annals of Statistics, 8, 598-617.

....notes and is continually changing, but feel free to grab a copy. If you have additions or corrections, please let me know. RG: This has NOT been updated since around Dec 96. 1 Network Representations Defined 1.1 General Properties of Conditional Independence Graphical Axioms of C.I. Daw79] Daw80] Spo80] GP88] Pea88b] Smi89] Smi90] Critical Graph Theoretical Properties: LSV84] Spe79] Hyper Markov laws: DL93b] HB94b] Mathematical properties of Markov Fields: Ish81] Lau82] Causal Independence: HB94b] 1.2 Bayesian Networks General overviews: Cha91] HH88] HBH91] ....

A. P. Dawid. Conditional independence for statistical operations. Annals of Statistics, 8:598--617, 1980.

....We can identify Y with a transition operator fl, mapping L 1 (P; F) into L 1 (P; G) identified by the analog of equality 42 , hflX; W i = hX; W i all W in L 1 (P; G) And then we can dispense with Y altogether and express conditioning properties purely in terms of a transition operator. Dawid (1980) chose something similar as the best way to deal with the general form of conditional independence. Finally, one can dispense with the interpretation of the domains of probability measures as families of random variables on a specific Omega set, and treat conditioning as transition map between ....

Dawid, A. P. (1980). Conditional independence for statistical operations. Ann. Statist. 8 598--617.

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Dawid, A. P. (1980a). Conditional independence for statistical operations. Ann. Statist . 8, 598--617. A technical study of CI, including for parametric statistical families.

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