Ignorable Common Information, Null sets and Basu’s First Theorem
Ernesto San Martı́n, Michel Mouchart · 2005
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.