D. Geiger, D. Heckerman, Parameter priors for directed acyclic graphical models and the characterization of several probability distributions, Annals of Statistics 5 (2002) 1412--1440. Home/Search Document Details and Download
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Structural Learning of Dynamic Bayesian Networks in Speech.. - Deviren (2001) (Correct)
....the parameters . An important point in the selection of the prior is to have a conjugate family so that the functional form remains the same in the presence of data (i.e. the prior and posterior pdfs have the same functional form) Construction of parameter priors for DAG modes is discussed in [14]. The initialization of the priors is another issue, which requires prior knowledge over the domain. 18] de nes a method to initialize parameter priors for BNs of discrete variables with multinomial distributions based on a set of assumptions. A similar method is extended to continuous case in ....
Dan Geiger and David Heckerman. Parameter priors for directed acyclic graphical models and the characterization of several probability distributions. Technical Report MSR-TR-98-67, Microsoft Research, Advanced Technology Division, 1999. ../geiger/tr-98-67.ps. 30
On Parameter Priors for Discrete DAG Models - Rusakov, Geiger (2000) (1 citation) Self-citation (Geiger) (Correct)
.... 7] In contrast, in a subsequent work, it was shown that for Gaussian DAG models, which consist of a recursive set of linear regression models, global independence alone dictates that the only feasible parameter prior is the Normal Wishart distribution, assuming models with at least three nodes [6]. It was thus natural to hypothesize that the proofs for discrete and continuous case can be unified and, as a result, the assumption of local independence will turn out to be redundant also in the characterization of the Dirichlet distribution. This work shows that, while global parameter ....
....distributions for binary valued network. This result extends the result stated in [5] for DAG models with two binary variables and demonstrates that global parameter independence assumption alone is not enough to ensure Dirichlet prior for networks of any size (contrary to the Gaussian DAG models, [6]) Theorem 4 Any distribution on Theta X , where X = X 1 ; Xn are binary random variables, that satisfies regularity (1) and global parameter independence assumptions is of the form p( Theta X ) C 2 4 Y x2f0;1g n ff x x 3 5 h Q x2A0 x Q x2A1 x (16) ....
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D. Geiger and D. Heckerman. Parameter priors for directed acyclic graphical models and the characterization of several probability distributions. To appear in Annals of Statistics, 2001.
Sparse Graphical Models for Exploring Gene - Expression Data Adrian (Correct)
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D. Geiger, D. Heckerman, Parameter priors for directed acyclic graphical models and the characterization of several probability distributions, Annals of Statistics 5 (2002) 1412--1440.
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