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The application of Bayesian techniques to astronomical data is generallynon-trivial because the fitting parameters can be strongly degenerated and theformal uncertainties are themselves uncertain. An example is provided by thecontradictory claims over the presence or absence of a universal accelerationscale (g$_\dagger$) in galaxies based on Bayesian fits to rotation curves. Toillustrate the situation, we present an analysis in which the Newtoniangravitational constant $G_N$ is allowed to vary from galaxy to galaxy whenfitting rotation curves from the SPARC database, in analogy to $g_{\dagger}$ inthe recently debated Bayesian analyses. When imposing flat priors on $G_N$, weobtain a wide distribution of $G_N$ which, taken at face value, would rule out$G_N$ as a universal constant with high statistical confidence. However,imposing an empirically motivated log-normal prior returns a virtually constant$G_N$ with no sacrifice in fit quality. This implies that the inference of avariable $G_N$ (or g$_{\dagger}$) is the result of the combined effect ofparameter degeneracies and unavoidable uncertainties in the error model. Whenthese effects are taken into account, the SPARC data are consistent with aconstant $G_{\rm N}$ (and constant $g_\dagger$).

A cautionary tale in fitting galaxy rotation curves with Bayesian techniques: does Newton's constant vary from galaxy to galaxy?