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Sensitivity to hyperprior parameters in Gaussian Bayesian networks

Gómez Villegas, Miguel Ángel and Main Yaque, Paloma and Navarro, H. and Susi García, Rosario (2010) Sensitivity to hyperprior parameters in Gaussian Bayesian networks. [ Cuadernos de Trabajo de la Escuela Universitaria de Estadística; nº 03/201, ]

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Abstract

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 later representation the paramenters 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 inteserested 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.


Item Type:Working Paper or Technical Report
Uncontrolled Keywords:Gaussian Bayesian networks, Kullback-Leibler divergence, Bayesian linear regression
Subjects:Sciences > Mathematics > Mathematical statistics
Sciences > Statistics > Operations research
Series Name:Cuadernos de Trabajo de la Escuela Universitaria de Estadística
Volume:
Number:03/201
ID Code:10941
Deposited On:30 Jun 2010 10:26
Last Modified:06 Feb 2014 08:53

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