On the likelihood ratio for source identification

Abstract

The general use of the likelihood ratio technique for source identification as applied to, for example, IRAS galaxies and radio sources, is discussed. This method is an optimal technique for source identification as long as the prior distributions of source magnitudes and position errors are moderately well known from other work, or can be estimated from the data using a control sample. A self-consistent formula is derived for identification reliability; it is shown to be exact where the prior is well known, and deals correctly with the case of multiple candidates. The discrepancies with previous work, due in general to calculating p(X/A) when in fact p(X/A,B) is implicitly meant, is explained. It is recommended that this method be treated as an adjunct to spectroscopic identifications rather than a substitute. When the reliability estimates are used, it is possible to optimize the efficiency of such identifications with minimum wastage of scarce telescope time.