Demonstration of how the proper motion likelihood (P(μ∣r, v), orange) combines with the velocity prior (P(v∣r), blue) to constrain the distance via Equation (A1), from a measured proper motion of 1 ± 0.25 mas yr⁻¹. This is shown for two different velocities, 10 and 30 km s⁻¹. The gray curve is the product of the orange and blue curves. The black dashed line is the integral in Equation (A1) computed for a continuous range of velocities. None of these functions are probability density functions in r, but all have been normalized to unit area over the range plotted.