Bayes solutions of some simple statistical decision problems
Oberbeck, Thomas Edmond
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Bayes solutions are obtained for some specific simple statistical decision problems which may be stated in the following practical terms. The result of a trial of a weapon system is valued as success (1) or failure (0) and p , the true probablility of success is unknown. Prior to testing, it is assumed that any value of p in the interval (0,1) is equally likely. Take as an estimate of p , the fraction, Pe of a finite number of trials which result in success. At the conclusion of testing, the weapon system is accepted (terminal decision d1) if Pe.> 0 , and it is rejected (terminal decision d2) if Pe < 0 , where 0 is a number in the interval (o,1) chosen by the experimenter. If Pe= 0 , either terminal decision may be made. A wrong decision may be made in two ways: (i) if the weapon system is accepted and the true p lies in an interval (0, [infinity]), where [inifnity] > 0 or (ii) if the weapon system is rejected and the true p lies in an interval (1 - b, 1) where 0 < 1-b . In this paper we consider only the case where [infinity and [beta] have the same value which we denote as 0 (symmetric case). The cost of wrong decision is defined in terms of a symmetric weight function, W(p,d1; 0), i = 1,2; W is simple or linear as defined below.
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