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 ofDutch Books.As an example, a newlow density based independence model is being developed, exhibiting a phase transition in the vacuum probability.
CITATION STYLE
Catalano, C., & Gandolfi, A. (2017). Partially independent random variables. In Springer Proceedings in Mathematics and Statistics (Vol. 190, pp. 33–56). Springer New York LLC. https://doi.org/10.1007/978-3-319-46310-0_3
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