Sequential Search for an Unknown Number of Objects of Nonuniform Size

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Abstract
This paper deals with a search model for allocating effort when there are many target objects of differing sizes present in a search area. All target objects are initially present in the search area and remain at least until discovered; no new objects are generated during the search process. Targets are not moveable. The search process is characterized by the quantity of search effort. The model describes the distribution of the number and sizes of target objects present. The probability of discovery is assumed proportional to object size. The paper gives many results, including the probability distribution of the number and sizes of discovered objects, and the prior and posterior distributions of the number of objects remaining undiscovered. Then it gives the method of maximum likelihood estimation of the model parameters, and solves the sequential decision problem of when to terminate the search process.

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