On the Compatibility of Conditional Normal Distributions

• Activity Number: 521
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Thomas Jyh-Ming Jiang*+ and Kun-Lin Kuo and Chwan-Chin Song and Lin-Yang Cheng
• Companies: National Chengchi University and Academia Sinica and National Chengchi University and National Chengchi University
• Keywords: compatible conditional distributions ; normal distributions ; degree of incompatibility

Abstract

The characterization of the bivariate density whose conditionals are univariate normal densities and its properties have been studied by Castillo and Galambos (1989), Gelman and Meng (1991), Arnold, Castillo, Sarabia and Gonzalez-Vega (2000), and among others. First, we will use a different approach to revisit its characterization and it can be seen that two compatible distributions have zero degree of incompatibility. However, two samples from two compatible conditional distributions are likely to have nonzero degree of incompatibility. Hence, second, we shall study the degree of incompatibility of sample conditional distributions. Generalization to the characterization of trivariate density whose conditionals are univariate normal densities is also investigated.