Conditional Specification with Exponential Power Distributions

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.

Keywords:

• Bayesian networks
• Conditionally specified distributions
• Exponential power distributions

Mathematics Subject Classification:

• Primary 62E10, 62E15
• Secondary 62H05