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

作者：Main P^*; Navarro H

来源：Reliability Engineering & System Safety, 2009, 94(5): 922-926.

DOI：10.1016/j.ress.2008.10.004

• Gaussian Bayesian networks
• Kullback-Leibler divergence
• Exponential power distribution
• Sensitivity analysis

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.

• 出版日期2009-5