2008/01/08 by Gert de Cooman, de Cooman, Gert, Erik Quaeghebeur +3
Arts and Humanities · Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #Epistemology, Ethics, and Metaphysics #FOS: Computer and information sciences #FOS: Mathematics #Logic, Reasoning, and Knowledge #Methodology (stat.ME) #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.0801.1265
1 figure. 26 pages. Submitted for publication
arxiv created 2008/01/08 · openalex publication_date 2008/01/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend de Finetti's (1937) 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 prove representation theorems in both the finite and the countable case, in terms of sampling without and with replacement, respectively. We also establish a convergence result for sample means of exchangeable sequences. Finally, we study and solve the problem of exchangeable natural extension: how to find the most conservative (point-wise smallest) coherent and exchangeable lower prevision that dominates a given lower prevision.