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We derive the form of the maximum likelihood (ML) estimate of the location of the scintillation point given the photomultiplier counts in an Anger Scintillation camera. This estimate is also Maximum a Posteriori (MAP) if the prior probability density on the scintillation point is uniform in the object plane. The form of the estimate suggests the possibility of an optical filtering implementation. We note that the ML estimate implies a solution that is remarkably similar to the "optimum position arithmetic" derived by Tanaka, et al.