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Convex geometry of finite exchangeable laws and de Finetti style representation with universal correlated corrections

Carlier, Guillaume; Friesecke, Gero; Vögler, Daniela (2022), Convex geometry of finite exchangeable laws and de Finetti style representation with universal correlated corrections, Probability Theory and Related Fields, p. 44. 10.1007/s00440-022-01115-2

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Type
Article accepté pour publication ou publié
Date
2022
Journal name
Probability Theory and Related Fields
Publisher
Springer
Published in
Paris
Pages
44
Publication identifier
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Author(s)
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Friesecke, Gero
Zentrum Mathematik [Munchen] [TUM]
Vögler, Daniela
Zentrum Mathematik [Munchen] [TUM]
Abstract (EN)
We present a novel analogue for finite exchangeable sequences of the de Finetti, Hewitt and Savage theorem and investigate its implications for multi-marginal optimal transport (MMOT) and Bayesian statistics. If (Z 1 , ..., Z N) is a finitely exchangeable sequence of N random variables taking values in some Polish space X, we show that the law µ k of the first k components has a representation of the form
Subjects / Keywords
N-representability; Finite exchangeability; de Finetti; Hewitt-Savage theorem; Multi-marginal optimal transport; Bayesian statistics; Extremal measures; Choquet theory