# Need a statistic for comparing “strength” of Markov blankets in a Bayesian network

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?

• You could start with a test of conditional independence (like the G-test or the chi-squared test): calculate the statistic, but stop before applying a threshold. You would get a p-value for how independent a node is of the network, given each separate Markov blanket, and compare the p-values generated by the tests of conditional independence. But please be aware this is abusing p-values. They aren't "scores" in the proper sense. – CamilB Jun 29 at 9:29