@article{DeBock20161,
title = "Representation theorems for partially exchangeable random variables ",
journal = "Fuzzy Sets and Systems ",
volume = "284",
number = "",
pages = "1 - 30",
year = "2016",
note = "Theme: Uncertainty and Copulas ",
issn = "0165-0114",
doi = "http://dx.doi.org/10.1016/j.fss.2014.10.027",
url = "http://www.sciencedirect.com/science/article/pii/S0165011414004837",
author = "Jasper De Bock and Arthur Van Camp and Márcio A. Diniz and Gert de Cooman",
keywords = "Partial exchangeability",
keywords = "Sets of desirable gambles",
keywords = "Lower previsions",
keywords = "de Finetti's representation theorem",
keywords = "Indifferent gambles ",
abstract = "Abstract We provide representation theorems for both finite and countable sequences of finite-valued random variables that are considered to be partially exchangeable. In their most general form, our results are presented in terms of sets of desirable gambles, a very general framework for modelling uncertainty. Its key advantages are that it allows for imprecision, is more expressive than almost every other imprecise-probabilistic framework and makes conditioning on events with (lower) probability zero non-problematic. We translate our results to more conventional, although less general frameworks as well: lower previsions, linear previsions and probability measures. The usual, precise-probabilistic representation theorems for partially exchangeable random variables are obtained as special cases. "
}