Exchangeable lower previsions
Gert de Cooman, Erik Quaeghebeur, Enrique Miranda
TL;DR
This paper generalizes de Finetti's exchangeability concept to beliefs modeled by coherent lower previsions, providing representation theorems for finite and countable sequences with implications for sampling methods.
Contribution
It introduces a novel extension of exchangeability to lower previsions and establishes foundational representation theorems for finite and infinite sequences.
Findings
Representation theorems for finite and countable exchangeable sequences
Connection between exchangeability and sampling without/with replacement
Extension of classical de Finetti's theorem to lower previsions
Abstract
We extend de Finetti's [Ann. Inst. H. Poincar\'{e} 7 (1937) 1--68] notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than (linear) previsions. We derive representation theorems in both the finite and countable cases, in terms of sampling without and with replacement, respectively.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.