Analyzing the effect of introducing a kurtosis parameter in Gaussian Bayesian networks

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Main Yaque, Paloma and Navarro Veguillas, Hilario (2009) Analyzing the effect of introducing a kurtosis parameter in Gaussian Bayesian networks. Reliability engineering & systems safety, 94 (5). pp. 922-926. ISSN 0951-8320

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Official URL: http://www.sciencedirect.com/science/article/pii/S0951832008002548




Abstract

Gaussian Bayesian networks are graphical models that represent the dependence structure of a multivariate normal random variable with a directed acyclic graph (DAG). In Gaussian Bayesian networks the output is usually the conditional distribution of some unknown variables of interest given a set of evidential nodes whose values are known. The problem of uncertainty about the assumption of normality is very common in applications. Thus a sensitivity analysis of the non-normality effect in our conclusions could be necessary. The aspect of non-normality to be considered is the tail behavior. In this line, the multivariate exponential power distribution is a family depending on a kurtosis parameter that goes from a leptokurtic to a platykurtic distribution with the normal as a mesokurtic distribution. Therefore a more general model can be considered using the multivariate exponential power distribution to describe the joint distribution of a Bayesian network, with a kurtosis parameter reflecting deviations from the normal distribution. The sensitivity of the conclusions to this perturbation is analyzed using the Kullback-Leibler divergence measure that provides an interesting formula to evaluate the effect.


Item Type:Article
Uncontrolled Keywords:Gaussian Bayesian networks; Kullback-Leibler divergence; Exponential power distribution; Sensitivity analysis;
Subjects:Sciences > Mathematics > Applied statistics
ID Code:16482
Deposited On:21 Sep 2012 08:20
Last Modified:29 Jun 2018 11:41

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