A detailed treatment of Doob's theorem

01/09/2018

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by   Jeffrey W. Miller, et al.

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Doob's theorem provides guarantees of consistent estimation and posterior consistency under very general conditions. Despite the limitation that it only guarantees consistency on a set with prior probability 1, for many models arising in practice, Doob's theorem is an easy way of showing that consistency will hold almost everywhere. In this article, we give a detailed proof of Doob's theorem.