Parameter Estimation with Incomplete a Priori Information; Photoelectron Counts

Abstract

Photoelectron counting experiments are considered. The object of the measurement is to determine parameters defining the state of a physical system characterized by a set of parameters {αi} on the basis of an observed set of photoncount numbers {nj}. Two types of parameters are involved: those that are to be determined, {αi}p (primary), and those that have impact on the estimation but are otherwise of no interest to the object of the measurement, {αi}s (secondary). The problem can be analyzed by investigating the relations between the conditional probabilities, p({αi}p,{αi}s|{nj}) and p({αi}p|{nj};{αi}s).