Exact and near compatibility of discrete conditional distributions
Computational Statistics & Data Analysis
Dependency networks for inference, collaborative filtering, and data visualization
The Journal of Machine Learning Research
Canonical representation of conditionally specified multivariate discrete distributions
Journal of Multivariate Analysis
Compatibility of discrete conditional distributions with structural zeros
Journal of Multivariate Analysis
The space of compatible full conditionals is a unimodular toric variety
Journal of Symbolic Computation
Gibbs ensembles for nearly compatible and incompatible conditional models
Computational Statistics & Data Analysis
A simple algorithm for checking compatibility among discrete conditional distributions
Computational Statistics & Data Analysis
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To deal with the compatibility issue of full conditional distributions of a (discrete) random vector, a graphical representation is introduced where a vertex corresponds to a configuration of the random vector and an edge connects two vertices if and only if the ratio of the probabilities of the two corresponding configurations is specified through one of the given full conditional distributions. Compatibility of the given full conditional distributions is equivalent to compatibility of the set of all specified probability ratios (called the ratio set) in the graphical representation. Characterizations of compatibility of the ratio set are presented. When the ratio set is compatible, the family of all probability distributions satisfying the specified probability ratios is shown to be the set of convex combinations of k probability distributions where k is the number of components of the underlying graph.