In this paper we investigate the task of parameter learning of Bayesian networks and, in particular, we deal with the prior uncertainty of learning using a Bayesian framework. Parameter learning is explored in the context of Bayesian inference and we subsequently introduce Bayes, constrained Bayes and robust Bayes parameter learning methods. Bayes and constrained Bayes estimates of parameters are obtained to meet the twin objective of simultaneous estimation and closeness between the histogram of the estimates and the posterior estimates of the parameter histogram. Treating the prior uncertainty, we consider some classes of prior distributions and derive simultaneous Posterior Regret Gamma Minimax estimates of parameters. Evaluation of the merits of the various procedures was done using synthetic data and a real clinical dataset.
"Constrained parameter estimation with uncertain priors for Bayesian networks." Electron. J. Statist. 11 (2) 4000 - 4032, 2017. https://doi.org/10.1214/17-EJS1350