Working with Bayesian networks. I take a given network structure and fit its parameters on data.
I am looking for a statistic based on those parameter estimates that allows me to compare Markov blankets within the network. I want this stat to reflect the strength of mutual dependence between all the nodes in the MB, in a way that is comparable to all the other MBs in the network. In the end, I want a visualization that looks like this heat map, where more yellow the MB the greater the strength of conditional dependence between the nodes that comprise it.
Using likelihood-based stats doesn't work because each MB contains different sets and numbers of variables. Two things I came up with were calculating total correlation calculated from probability queries on the fitted network. The variables are discrete, so another way I thought of is calculating an estimate for Bayes error rate of a node given its MB, as a quantification for how well an MB can predict its core node.
But I feel this can't be a new problem. Perhaps there is a simpler way stat out there? One that I can easily explain to non-quants?