Atomic Intersection of s-Fields and Some of Its Consequences

Patrizia Berti, Luca Pratelli and Pietro Rigo
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Patrizia Berti: Università di Modena e Reggio Emilia
Luca Pratelli: Accademia Navale di Livorno
Pietro Rigo: Department of Economics and Quantitative Methods, University of Pavia

No 96, Quaderni di Dipartimento from University of Pavia, Department of Economics and Quantitative Methods

Abstract: Let (omega,F,P) be a probability space. For each G in F, define G as the s-field generated by G and those sets f in F satisfying P(f) in {0, 1}. Conditions for P to be atomic on the intersection of the complements of Ai for i=1,..,k, with A1, . . . ,Ak in F sub-s-fields, are given. Conditions for P to be 0-1-valued on the intersection of the complements of Ai for i=1,..,k are given as well. These conditions are useful in various fields, including Gibbs sampling, iterated conditional expectations and the intersection property.

Keywords: Atomic probability measure; Gibbs sampling; Graphical models; Intersection property; Iterated conditional expectations. (search for similar items in EconPapers)
Pages: 13 pages
Date: 2009-05
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