Main Yaque, Paloma and Navarro Veguillas, Hilario
(2010)
*Conditional Specification with Exponential Power Distributions.*
Communications in statistics. Theory and methods, 39
(12).
pp. 2231-2240.
ISSN 0361-0926

PDF
Restricted to Repository staff only until 31 December 2020. 118kB |

Official URL: http://www.tandfonline.com/doi/abs/10.1080/03610920903009392

## Abstract

The problem of modeling Bayesian networks with continuous nodes deals with discrete approximations and conditional linear Gaussian models. In this article we have considered the possibility of using the exponential power family as conditional probability densities. It will be shown that for some platikurtic conditional distributions in this family, conditional regression functions are constant. These results give conditions to avoid compatibility problems when distributions with lighter tails than the normal are used in the description of conditional densities to specify joint densities, like in Bayesian networks.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Bayesian networks; Conditionally specified distributions; Exponential power distributions; |

Subjects: | Sciences > Mathematics > Applied statistics |

ID Code: | 16462 |

References: | Abramowitz, M., Stegun, I. (1968). Handbook of Mathematical Functions. New York: Dover Publications. Aczel, J. (1966). Lectures on Functional Equations and Their Applications. New York:Academic Press. Arnold,B.C.,Castillo,E.,Sarabia,J.(1999).Conditional Specification of Statistical Models.New York:Springer-Verlag. Arnold, B. C.,Castillo, E.,Sarabia, J.(2001). Conditionally specified distributions:an introduction. Stat. Sci. 16:249–274. Arnold, B. C., Castillo, E., Sarabia, J., González-Vega, L. (2000). Multiple modes in densities with normal conditionals. Stat. Probab. Lett. 49:355–363. Arnold, B. C., Press, J. (1989). Compatible conditional distributions. J. Am. Stat. Assoc. 84:152–156. Arnold, B., Strauss, D. (1991). Bivariate distributions with conditionals in prescribed exponential families. J. Roy. Stat. Soc. B 53:365–375. Bhattacharyya, A. (1943). On some sets of sufficient conditions leading to the normal bivariate distribution. Sankhya 6:399–406. Box, G. E. P., Tiao, G. C. (1973). Bayesian Inference in Statistical Analysis. New York: Wiley. Castillo, E., Gutiérrez, J. M., Hadi, A. S. (1997). Expert Systems and Probabilistic Network Models. New York: Springer Verlag. Cowell, R. G., Dawid, A. P., Lauritzen, S. L., Spiegelhalter, D. J. (2007). Probabilistic Networks and Expert Systems. New York: Springer Verlag. DiCiccio, T. J., Monti, A. C. (2004). Inferential aspects of the skew exponential power distribution. J. Am. Stat. Assoc. 99:439–450. Gómez, E., Gómez-Villegas, M. A., Marín, J. M. (1998). A multivariate generalization of the power exponential family of distributions. Comm. Stat. Theor. Meth. 27:589–600. Gómez, E., Gómez-Villegas, M. A., Marín, J. M. (2002). Continuous elliptical and exponential power linear dynamic models. J. Multivariate Anal. 83:22–36. Jensen, F. V., Nielsen, T. D. (2007). Bayesian Networks and Decision Graphs. 2nd ed.New York: Springer-Verlag. Kuwana, Y., Kariya, T. (1991). LBI tests for multivariate normality in exponential power distributions.J. Multivariate Anal. 39:117–134. Lauritzen, S. L., Spiegelhalter, D. J. (1988). Local computations with probabilities on graphical structures and their application to expert systems.J.Roy.Stat.Soc.B 50 :157–224. Main, P., Navarro, H. (2007). Exponential power conditional distributions. Technical Report 1-07. Department of Statistics and Operations Research, Universidad Complutense of Madrid. Main, P., Navarro, H. (2009). Analyzing the effect of introducing a kurtosis parameter in Gaussian Bayesian networks. Reliab. Eng. Syst. Saf. 94:922–926. Marín, J. M. (2000). A robust version of the dynamic linear model with an econometric application. In: Rios, D., Ruggeri, F., eds. Robust Bayesian Analysis(pp. 373–383).New York: Springer. Mineo, A. M., Ruggieri, M. (2005). A software tool for the exponential power distribution:the normalp package. J. Stat. Software 12:4. Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference.San Mateo, CA: Morgan Kaufmann. West, M. (1987). On scale mixtures of normal distributions. Biometrika 74:646–648. |

Deposited On: | 20 Sep 2012 09:03 |

Last Modified: | 07 Feb 2014 09:29 |

Repository Staff Only: item control page