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Keywords:
sequential analysis; discrete-time stochastic process; dependent observations; statistical decision problem; Bayes decision; randomized stopping time; optimal stopping rule; existence and uniqueness of optimal sequential decision procedure
sequential analysis; discrete-time stochastic process; dependent observations; statistical decision problem; Bayes decision; randomized stopping time; optimal stopping rule; existence and uniqueness of optimal sequential decision procedure
Summary:
In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does not exceed some given bound. We characterize the form of optimal sequential stopping rules in this problem. In particular, we have a characterization of the form of optimal sequential decision procedures when the Bayesian risk includes both the loss due to incorrect decision and the cost of observations.
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