A cautionary tale in fitting galaxy rotation curves with Bayesian techniques: does Newton’s constant vary from galaxy to galaxy?. (arXiv:2101.11644v2 [astro-ph.GA] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Li_P/0/1/0/all/0/1">Pengfei Li</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Lelli_F/0/1/0/all/0/1">Federico Lelli</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+McGaugh_S/0/1/0/all/0/1">Stacy McGaugh</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Schombert_J/0/1/0/all/0/1">James Schombert</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Chae_K/0/1/0/all/0/1">Kyu-Hyun Chae</a>

The application of Bayesian techniques to astronomical data is generally
non-trivial because the fitting parameters can be strongly degenerated and the
formal uncertainties are themselves uncertain. An example is provided by the
contradictory claims over the presence or absence of a universal acceleration
scale (g$_dagger$) in galaxies based on Bayesian fits to rotation curves. To
illustrate the situation, we present an analysis in which the Newtonian
gravitational constant $G_N$ is allowed to vary from galaxy to galaxy when
fitting rotation curves from the SPARC database, in analogy to $g_{dagger}$ in
the recently debated Bayesian analyses. When imposing flat priors on $G_N$, we
obtain 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 a
variable $G_N$ (or g$_{dagger}$) is the result of the combined effect of
parameter degeneracies and unavoidable uncertainties in the error model. When
these effects are taken into account, the SPARC data are consistent with a
constant $G_{rm N}$ (and constant $g_dagger$).

The application of Bayesian techniques to astronomical data is generally
non-trivial because the fitting parameters can be strongly degenerated and the
formal uncertainties are themselves uncertain. An example is provided by the
contradictory claims over the presence or absence of a universal acceleration
scale (g$_dagger$) in galaxies based on Bayesian fits to rotation curves. To
illustrate the situation, we present an analysis in which the Newtonian
gravitational constant $G_N$ is allowed to vary from galaxy to galaxy when
fitting rotation curves from the SPARC database, in analogy to $g_{dagger}$ in
the recently debated Bayesian analyses. When imposing flat priors on $G_N$, we
obtain 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 a
variable $G_N$ (or g$_{dagger}$) is the result of the combined effect of
parameter degeneracies and unavoidable uncertainties in the error model. When
these effects are taken into account, the SPARC data are consistent with a
constant $G_{rm N}$ (and constant $g_dagger$).

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