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A Characterization of the Dirichlet Distribution with Application to Learning Bayesian Networks (1995)  (Make Corrections)  (7 citations)
Dan Geiger, David Heckerman



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Abstract: this technical claim is that in order to find all positive integrable functions that satisfy Eq. 9, it is permissible to take any derivative at any point in the domain because it exists. By setting z ij = 1=k, for all i and j, in Equation 9 we get that f 0 (y 1 ; : : : ; y n\Gamma1 ) is proportional to (Update)

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.... of Conjugacy: Dawid s response to [LS88] Continuous Belief Function Densities: WD94b] WD94a] others: AFS94] KSC84] GH94a] GH95a] Ken86] 1.10 Philosophical Issues 1.10.1 Causality and Control refs: Pea88a] Pea94b] Pea94a] Pea95b] Pea95a] SGS93] DS93]...

...Namely, the parameter distributions before and after data are seen are in the same family: the Dirichlet family. Geiger and Heckerman (1995) provide a characterization of the Dirichlet distribution, which shows that the fifth assumption is implied from the first three...

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BibTeX entry:   (Update)

D. Geiger and D. Heckerman, A characterization of the Dirichlet distribution with application to learning Bayesian networks. Proceedings of Eleventh Conference on Uncertainty in Artificial Intelligence, Montreal, QU, 196--207, August 1995. Morgan Kaufmann. http://citeseer.ist.psu.edu/article/geiger95characterization.html   More

@inproceedings{ geigercharacterization,
    author = "Dan Geiger and David Heckerman",
    title = "A Characterization of the {Dirichlet} Distribution with Application to Learning {Bayesian} Networks",
    pages = "196--207",
    url = "citeseer.ist.psu.edu/article/geiger95characterization.html" }
Citations (may not include all citations):
1543   Probabilistic Reasoning in Intelligent Systems: Networks of .. (context) - Pearl - 1988
351   Learning Bayesian Networks: The combination of knowledge and.. - Heckerman, Geiger et al. - 1994
181   Optimal statistical decisions (context) - DeGroot
148   Bayesian analysis in expert systems (context) - Spiegelhalter, Dawid et al. - 1993
118   Sequential updating of conditional probabilities on directed.. (context) - Spiegelhalter, Lauritzen - 1990
84   Theory refinement on Bayesian networks - Buntine - 1991
52   Hyper Markov laws in statistical analysis of decomposable gr.. (context) - Dawid, Lauritzen - 1993
40   Learning Gaussian Networks - Geiger, Heckerman - 1994
25   Lectures on functional equations and their applications (context) - Acz'el - 1966
22   Wiley and Sons (context) - Wilks, Statistics
18   Learning Bayesian Networks: A unification for discrete and G.. (context) - Heckerman, Geiger
12   A characterization of the Dirichlet distribution through glo.. - Geiger, Heckerman - 1995
8   Learning Bayesian networks - Heckerman, Geiger et al. - 1995



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