= Proper distance prior for parallax inference
{title2=$p(r)\propto r^2e^{-r/L},\quad r>0$}
For a <Gaussian> measured <stellar parallax>, the <likelihood> at distance $r$ approaches a nonzero constant as $r\to\infty$. An unbounded spatial-volume <prior> proportional to $r^2$ therefore gives an improper <posterior>. A finite survey/population model or a decaying <density> is needed. The illustrative proper <prior> displayed has normalizing constant $1/(2L^3)$; its scale is a model choice requiring justification, not a new measured datum. <prior> sensitivity is especially important at low parallax signal-to-noise.
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