On compatibility of discrete full conditional distributions: A graphical representation approach

Compatibility of distributions in probabilistic models: an algebraic frame and some characterizations

“…48-49;Slavkovic and Sullivant, 2006, pp. 198 and 206;Yao, Chen and Wang, 2014). In particular, Slavkovic and Sullivant (2006) address the compatibility problem using tools from the algebra of polynomials, show that the compatibility between any two or more saturated probability kernels can be characterized in terms of a system of binomial equations, and come to conclude that for any fixed combination {(Y 1 |X 1 ), .…”

“…, m. Another limitation is its expensiveness, as the acceptance of the compatibility hypothesis requires a test (with positive result) on each cycle within the graph (T • , E, R). Algorithms may be devised to simplify this testing process by exploiting redundancies implicit in the graph (Wang and Kuo, 2010;Kuo and Wang, 2011;Yao, Chen and Wang, 2014). Lastly we remark that, of the cases covered by Theorem 3, special notice should be given to the case in which the conditioned variables Y 1 , .…”

An alternative approach for compatibility of two discrete conditional distributions

“…Wang (2012) compares the performance of three methods for checking compatibility of discrete conditional distributions. Yao et al (2014) propose a graphical approach for checking compatibility of discrete conditional distributions. They introduce a graphical representation "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".…”