Sankhya: The Indian Journal of Statistics

2005, Volume 67, Pt. 4, 674--698

Ignorable Common Information, Null Sets and Basu's First Theorem

Ernesto San Mart\'{\i}n, Pontificia Universidad Cat\'olica de Chile, Chile
Michel Mouchart and Jean-Marie Rolin, Universit\'e Catholique de Louvain, Belgium

SUMMARY. This paper deals with the Intersection Property, or Basu's First Theorem, which is valid under a condition of no common information, also known as measurable separability. After formalizing this notion, the paper reviews general properties and give operational characterizations in two topical cases: the finite one and the multivariate normal one. The paper concludes discussing the relevance of these characterizations for different fields as graphical models, zero entries in contingency tables, causal analysis and estimability in Markov processes.

AMS (2000) subject classification. 62B99.

Key words and phrases. Common information, conditional independence, forbidden states, measurable separability, structural zeros.

Full paper (PDF)