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I discuss an issue arising in analyzing data from astronomical surveys:accounting for measurement uncertainties in the properties of individualsources detected in a survey when making inferences about the entire populationof sources. Source uncertainties require the analyst to introduce unknown``incidental'' parameters for each source. The number of parameters thus growswith the size of the sample, and standard theorems guaranteeing asymptoticconvergence of maximum likelihood estimates fail in such settings. From theBayesian point of view, the missing ingredient in such analyses is accountingfor the volume in the incidental parameter space via marginalization. I usesimple simulations, motivated by modeling the distribution of trans-Neptunianobjects surveyed in the outer solar system, to study the effects of sourceuncertainties on inferences. The simulations show that current non-Bayesianmethods for handling source uncertainties (ignoring them, or using an ad hocincidental parameter integration) produce incorrect inferences, with errorsthat grow more severe with increasing sample size. In contrast, accounting forsource uncertainty via marginalization leads to sound inferences for any samplesize.Comment: 12 pages, 5 figures; to appear in Bayesian Inference And Maximum  Entropy Methods In Science And Engineering: 24th International Workshop,  Garching, Germany, 2004; ed. Volker Dose et al. (AIP Conference Proceedings  Series

Accounting for Source Uncertainties in Analyses of Astronomical Survey Data