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2017 Constrained parameter estimation with uncertain priors for Bayesian networks
Ali Karimnezhad, Peter J. F. Lucas, Ahmad Parsian
Electron. J. Statist. 11(2): 4000-4032 (2017). DOI: 10.1214/17-EJS1350


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.


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Ali Karimnezhad. Peter J. F. Lucas. Ahmad Parsian. "Constrained parameter estimation with uncertain priors for Bayesian networks." Electron. J. Statist. 11 (2) 4000 - 4032, 2017.


Received: 1 January 2017; Published: 2017
First available in Project Euclid: 19 October 2017

zbMATH: 1382.62007
MathSciNet: MR3714306
Digital Object Identifier: 10.1214/17-EJS1350

Primary: 62C10 , 62F15
Secondary: 62F30 , 62F35

Keywords: Bayesian networks , constrained Bayes estimation , Directed acyclic graph , posterior regret , robust Bayesian learning


Vol.11 • No. 2 • 2017
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