Response by Herman L. Marshall

Abstract

I am very interested in seeing how the Bayes rule approach might be applied to the problem I have outlined, but the particular analysis Prof. Gleser performed appears to be inapplicable here. The critical step is in the definition of the quantity p which represents the fraction of all tested cells that have a source in them. The value of this quantity is unknowable in the general astronomical survey because it depends on the extrapolation of the intrinsic source distribution to (effectively) zero flux, which may be too far below the survey limit to be valid. The method I outlined can be applied once the total number of sources in the survey itself is known or can be estimated and depends only weakly on this number. The only requirement is that the fitted relation between source number and flux can be extrapolated a relatively short ways below the survey limit and depends somewhat on the steepness of the relation. Details of this extrapolation were investigated by Murdoch et al. (1973, see text). It is an interesting question as to whether the Bayes formulation can be applied to analyses of surveys into unknown territory. My statements concerning desiderata governing survey completeness were directed at the unknowability of the intrinsic fluxes for specific sources; the prior information that one may have before a survey is performed is certainly useful in the method I described.