Need a statistic for comparing "strength" of Markov blankets in a Bayesian network - Cross Validated most recent 30 from stats.stackexchange.com 2019-08-25T13:47:21Z https://stats.stackexchange.com/feeds/question/141516 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://stats.stackexchange.com/q/141516 1 Need a statistic for comparing "strength" of Markov blankets in a Bayesian network Count Zero https://stats.stackexchange.com/users/29336 2015-03-12T22:15:00Z 2015-03-12T22:15:00Z <p>Working with Bayesian networks. I take a given network structure and fit its parameters on data.</p> <p>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 <a href="https://imgur.com/SzyWP3D" rel="nofollow noreferrer">heat map</a>, where more yellow the MB the greater the strength of conditional dependence between the nodes that comprise it.</p> <p>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 <a href="https://en.wikipedia.org/wiki/Total_correlation" rel="nofollow noreferrer">total correlation</a> 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.</p> <p>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?</p>