Distributions of means (left), modes (centre), and medians (right) for a series of 10⁴ posteriors calculated for a star at a true distance of 100 pc and f = 0.2, and observed parallaxes drawn at random from the corresponding Gaussian distribution. Posteriors are inferred with a uniform density prior truncated at 1 kpc (grey) or with a uniform density with exponential decay prior and length scale 1.35 kpc (blue). The red vertical line marks the true parallax; the grey and blue lines correspond to the expected value (mean) of each distribution (same colours as for the histograms).