Bulgeless Evolution And the Rise of Discs (BEARD) - III. A numerical simulation view of satellites around Milky-Way analogues

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Volume 709 (May 2026)

A&A, 709 (2026) A125

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Table 2.

Results from the GLM regression.

Model		β₀	β₁	β₂	α	ΔELPD

Priors		𝒩(0, 10²)			HalfCauchy(1)
NB	(Eq. 1)	$β_{0} = 0 . 52_{- 0.10}^{+ 0.09}$ $Mathematical equation: $ \beta_{0} = 0.52_{-0.10}^{+0.09} $$	$β_{1} = 0 . 76_{- 0.05}^{+ 0.05}$ $Mathematical equation: $ \beta_{1} = 0.76_{-0.05}^{+0.05} $$		$α = 9 . 4_{- 3.0}^{+ 3.3}$ $Mathematical equation: $ \alpha = 9.4_{-3.0}^{+3.3} $$	0
NB with B/T dependence	(Eq. 2)	$β_{0} = 0 . 53_{- 0.10}^{+ 0.09}$ $Mathematical equation: $ \beta_{0} = 0.53_{-0.10}^{+0.09} $$	$β_{1} = 0 . 74_{- 0.07}^{+ 0.07}$ $Mathematical equation: $ \beta_{1} = 0.74_{-0.07}^{+0.07} $$	$β_{2} = 0 . 15_{- 0.23}^{+ 0.23}$ $Mathematical equation: $ \beta_{2} = 0.15_{-0.23}^{+0.23} $$	$α = 9 . 5_{- 3.3}^{+ 3.4}$ $Mathematical equation: $ \alpha = 9.5_{-3.3}^{+3.4} $$	0.25

Poisson with B/T dependence	(Eq. 2)	$β_{0} = 0 . 51_{- 0.08}^{+ 0.08}$ $Mathematical equation: $ \beta_{0} = 0.51_{-0.08}^{+0.08} $$	$β_{1} = 0 . 74_{- 0.05}^{+ 0.05}$ $Mathematical equation: $ \beta_{1} = 0.74_{-0.05}^{+0.05} $$	$β_{2} = 0 . 20_{- 0.15}^{+ 0.15}$ $Mathematical equation: $ \beta_{2} = 0.20_{-0.15}^{+0.15} $$		45.06
Poisson	(Eq. 1)	$β_{0} = 0 . 51_{- 0.08}^{+ 0.08}$ $Mathematical equation: $ \beta_{0} = 0.51_{-0.08}^{+0.08} $$	$β_{1} = 0 . 77_{- 0.04}^{+ 0.04}$ $Mathematical equation: $ \beta_{1} = 0.77_{-0.04}^{+0.04} $$			46.76

Notes. Two first rows using the negative binomial likelihood, while the third and fourth ones use Poisson likelihood. Each column indicates one of the parameters of the fit. The over dispersion parameter of the negative binomial regression is α. Models are sorted by the expected log pointwise predictive density (ELPD). Poisson regression can be clearly ruled out. Both negative binomial regression models have similar score according to ELPD, moreover, the interaction term (β₂) is compatible with 0 within the 95% high density interval of the posterior.

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