Bayes' model of the best-choice problem with disorder (Q413926)

Summary: We consider the best-choice problem with disorder and imperfect observations. The decision maker observes sequentially a known number of i.i.d random variables from a known distribution with the object of choosing the largest. At a random time the distribution law of observations is changed. The random variables cannot be perfectly observed. Each time a random variable is sampled the decision maker is informed only whether it is greater than or less than some level specified by him. The decision maker can choose at most one of the observations. An optimal rule is derived in the class of Bayes strategies.