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Suppose X₁, X₂, are independent random variables such that for some unknown, each of X₁, , X - ₁ is distributed according to F₀, while X_, X + ₁, are all distributed according to F₁. We prove a result of Moustakides that claims that the CUSUM procedures are optimal in the sense of Lorden. We do that by proving that the procedures are Bayes for some stochastic mechanism of generating.
Ya’acov Ritov (Sat,) studied this question.
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