Sensitivity to hyperprior parameters in Gaussian Bayesian networks

Resumen

Our focus is on learning Gaussian Bayesian networks (GBNs) from data. In GBNs the multivariate normal joint distribution can be alternatively specified by the normal regression models of each variable given its parents in the DAG (directed acyclic graph). In the latter representation the parameters are the mean vector, the regression coefficients and the corresponding conditional variances. The problem of Bayesian learning in this context has been handled with different approximations, all of them concerning the use of different priors for the parameters considered. We work with the most usual prior given by the normal/inverse gamma form. In this setting we are interested in evaluating the effect of prior hyperparameters choice on posterior distribution. The Kullback-Leibler divergence measure is used as a tool to define local sensitivity comparing the prior and posterior deviations. This method can be useful to decide the values to be chosen for the hyperparameters.