The classical parallax-calibration problem combines measurement errors with the greater volume available at larger distances. A locally uniform spatial population has , which transforms under to on the valid distance interval. Parallax cuts and the nonlinear conversion to luminosity can bias calibration samples. A correction is not universal: the population model, selection information and inferential target must be specified. Distinguish the repeated-sampling bias of a selected sample from inference for a particular star using a justified prior.[ref]
On the Use of Trigonometric Parallaxes for the Calibration of Luminosity Systems: Theory by T. E. Lutz and D. H. Kelker. PASP 85, 573–578; classical calibration model
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