Left: Comparison between the true formation times and the estimated posterior mean in HORIZON-AGN. Perfect inference would lie on the (blue) diagonal line. Our method yields an unbiased estimator with regard to HORIZON-AGN for all timescales. Right: Assessment of the estimated uncertainty calibration with the credibility level on the x-axis, and the realised coverage on the y-axis. For each level (50%, 68%, and 95%), the true value lay in the estimated credibility interval slightly more often than the expected level. A perfect uncertainty calibration would be on the blue diagonal. Our estimator is well calibrated.