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OPTIMUM SEQUENTIAL SEARCH WITH DISCRETE LOCATIONS AND RANDOM ACCEPTANCE ERRORS.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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Much work has been done in search theory. However, very little effort has occurred where an objects presence at a location can be accepted when no object is present there. The case analyzed is of this type. The number of locations is finite, a single object is stationary at one location, and only one location is observed each step of the search. The objects location has a known prior probability distribution. Also known are the conditional probability of acceptance given the objects absence small and the conditional probability of rejection given the objects presence not too large these probabilities remain fixed for all searching and locations. The optimum sequential search policy specifies that the next location observed is one with the largest posterior probability of the objects presence evaluated after each step from Bayes Rule and that the object is at the first location where acceptance occurs. Placement at the first acceptance seems appropriate when the conditional probability of acceptance given the objects absence is sufficiently small. The policy is optimum in that, for any number of steps, it minimizes the probability of no acceptances and, simultaneously, maximizes the probability that an acceptance occurs and the object is accurately located. Search always terminates with probability one. Optimum truncated sequential policies are also considered. Methods are given for evaluating some pertinent properties and for investigating the possibility that no object occurs at any location. Author
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