Some statistical problems inherent in radioactive-source detection. [Searching for lost radiation source with moving detector system]

Some of the statistical questions associated with problems of detecting random-point-process signals embedded in random-point-process noise are examined. An example of such a problem is that of searching for a lost radioactive source with a moving detection system. The emphasis is on theoretical questions, but some experimental and Monte Carlo results are used to test the theoretical results. Several idealized binary decision problems are treated by starting with simple, specific situations and progressing toward more general problems. This sequence of decision problems culminates in the minimum-cost-expectation rule for deciding between two Poisson processes with arbitrary intensity functions. As an example, this rule is then specialized to the detector-passing-a-point-source decision problem. Finally, Monte Carlo techniques are used to develop and test one estimation procedure: the maximum-likelihood estimation of a parameter in the intensity function of a Poisson process. For the Monte Carlo test this estimation procedure is specialized to the detector-passing-a-point-source case. Introductory material from probability theory is included so as to make the report accessible to those not especially conversant with probabilistic concepts and methods. 16 figures.