are also presented in Table \[tab:results\].

Evaluating the posterior distributions {#sec:posteriors}
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To understand how well we constrain the parameters in our model, we compare the posterior distributions with the prior distributions. We perform this exercise in Fig. \[fig:magr\_params\], where we show the posterior medians and uncertainties for five free parameters in our model ($A_V$, $R_V$, Age, \[Fe/H\], $z$) as a function of $m_r$, the apparent magnitude of the galaxies according to the SMUDGes measurements. Overall, the fitting is better constrained, i.e., is restricted to a narrower range of values in the posterior distribution, for the brighter sources ($m_r\lesssim 19$), while the posterior distributions tend to be more similar to the prior distribution for the fainter sources ($m_r\gtrsim 19$). We discuss the results for the individual parameters below.

The extinction law parameters have limited impact on the optical SED shape of the UDGs, and no strong dust attenuation was required to fit the models. The median total extinction of $A_V\approx 0.1-0.2$ is recovered in all cases, whereas the total-to-selective extinction $R_V$ is mostly unchanged from the prior distribution. In practice, both parameters have the role of nuisance parameters in our analysis, as they are not of direct interest for this 