Abstract
We study collections of random variables characterized by independence requirements assigned for only a fraction of the joint values of the variables. Such classes of random variables generalize various known models, like one-dependent processes. We determine existence conditions, showing that existence is decidable, and then interpret such conditions in terms of Dutch Books. As an example, a new low density based independence model is being developed, exhibiting a phase transition in the vacuum probability.
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Catalano, C., Gandolfi, A. (2017). Partially Independent Random Variables. In: Abualrub, T., Jarrah, A., Kallel, S., Sulieman, H. (eds) Mathematics Across Contemporary Sciences. AUS-ICMS 2015. Springer Proceedings in Mathematics & Statistics, vol 190. Springer, Cham. https://doi.org/10.1007/978-3-319-46310-0_3
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DOI: https://doi.org/10.1007/978-3-319-46310-0_3
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