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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Restringido a Repository staff only hasta 31 December 2020. 521kB |

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 |
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Uncontrolled Keywords: | Gaussian Bayesian networks; Kullback-Leibler divergence; Exponential power distribution; Sensitivity analysis; |

Subjects: | Sciences > Mathematics > Applied statistics |

ID Code: | 16482 |

References: | Pearl J. Probabilistic reasoning in intelligent systems. Morgan Publishers, Inc.; 1988. Jensen FV. An introduction to Bayesian networks. NY: Springer; 1996. Lauritzen SL, Spiegelhalter DJ. Local computation with probabilities in graphical structures and their applications to expert systems. J R Stat Soc B 1988;50(2):154–227. Li Z, D’Ambrosio B. Efficient inference in Bayes networks as a combinatorial optimization problem. Int J Approx Reason 1994;11:55–81. Batchelor C, Cain J. Application of belief networks to water management studies. Agric Water Manage 1999;40(1):51–7. Cowell R. FINEX: a probabilistic expert system for forensic identification. Forensic Sci Int 2003;134:196–206. Friedman N, et al. Using Bayesian networks to analyze expression data. In: Proceedings of the fourth annual international conference on computational molecular biology; 2000. Langseth L, Portinale L. Bayesian networks in reliability. Reliab Eng Syst Safety 2007;92(1):92–108. Gómez E, Gómez-Villegas MA, Marín JM. A multivariate generalization of the power exponential family of distributions. Commun Stat 1998;B27:589–600. Kullback S, Leibler R. On information and sufficiency. Ann Stat 1951;22: 79–86. Box GEP, Tiao GC. Bayesian inference in statistical analysis. New York, NY: Wiley; 1992. Castillo E, Gutie´ rrez JM, Hadi AS. Sensitivity analysis in discrete Bayesian networks. IEEE Trans Syst Man Cybern 1997;26(7):412–23. Laskey KB. Sensitivity analysis for probability assesments in Bayesian networks. IEEE Trans Syst Man Cybern 1995;25:412–23. Castillo E, Kjærulff U. Sensitivity analysis in Gaussian Bayesian networks using a symbolic-numerical technique. Reliab Eng Syst Safety 2003;79(2): 139–48. Gómez-Villegas MA, Main P, Susi R. Sensitivity analysis in Gaussian Bayesian networks using a divergence measure. Commun Stat 2007;B36:523–39. Abramowitz M, Stegun I. Handbook of mathematical functions with formulas, graphs, and mathematical tables. In: Abramowitz M, Stegun IA, editors. Reprint of the 1972 edition. New York, NY: Dover Publications, Inc; 1992. |

Deposited On: | 21 Sep 2012 08:20 |

Last Modified: | 08 Jul 2015 08:08 |

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