On the σ-Algebraic Realization Problem

Michel Mouchart () and Jean-Marie Rolin
Additional contact information
Michel Mouchart: Université Catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences
Jean-Marie Rolin: Université Catholique de Louvain, Institut de Statistique

Chapter Chapter 1 in Nonparametric Bayesian Inference, 2024, pp 3-17 from Springer

Abstract: Abstract Given two σ $$\sigma $$ -algebras ℳ 1 $$\mathcal {M}_1$$ and ℳ 2 $$\mathcal {M}_2$$ , necessary and sufficient conditions are given for a σ $$\sigma $$ -algebra ℳ 3 $$\mathcal {M}_3$$ to minimally make ℳ 1 $$\mathcal {M}_1$$ and ℳ 2 $$\mathcal {M}_2$$ conditionally independent. Representations in terms of projections among σ $$\sigma $$ -algebras are derived from those conditions. A constructive algorithm is sketched. The concepts of weak and strong identification among σ $$\sigma $$ -algebras are shown to be a crucial tool; in particular, minimal splitting is in-between.

Date: 2024
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-61329-6_1

Ordering information: This item can be ordered from
http://www.springer.com/9783031613296

DOI: 10.1007/978-3-031-61329-6_1

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().