Oh what a tangled web we weave…
..when first we practice frequentist statistics!
I couldn’t resist a quick post directing you to a short paper on the arXiv with the following abstract:
I use archival data to measure the mass of the central black hole in NGC 4526, M = (4.70 +- 0.14) X 10^8 Msun. This 3% error bar is the most precise for an extra-galactic black hole and is close to the precision obtained for Sgr A* in the Milky Way. The factor 7 improvement over the previous measurement is entirely due to correction of a mathematical error, an error that I suggest may be common among astronomers.
The “mathematical error” quoted in the abstract involves using chi-squared-per-degree-of-freedom instead of chi-squared instead of the full likelihood function instead of the proper, Bayesian, posterior probability. The best way to avoid such confusion is to do things properly in the first place. That way you can also fold in errors on the distance to the black hole, etc etc…Follow @telescoper