= Lutz-Kelker bias
{c}
{title2=$p(\varpi)\propto\varpi^{-4}$ for a locally uniform spatial population}
The classical parallax-calibration problem combines measurement errors with the greater volume available at larger distances. A locally uniform spatial population has $p(r)\propto r^2$, which transforms under $r=1/\varpi$ to $p(\varpi)\propto\varpi^{-4}$ 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>.<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]{ref}
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