radius of $R_e \ge 5$ kpc, which is larger than most UDGs found so far . We conclude that it is very unlikely that many of our candidates lie at $z > 0.04$. Based on these considerations, we use the prior

$$z\sim \textrm{HalfNormal}(0.03^2)\text{,}$$

where we adopt the half-normal distribution to restrict the redshifts to positive values, and we assume a variance of $0.03^2$. In practice, this prior implies a median redshift $z\approx 0.02$, similar to Coma, with peak probability at $z=0$.

Regarding the dust attenuation, our data include only wavelengths $\lambda > 3000$ for low redshift galaxies, avoiding the 2175 bump [@1965ApJ...142.1683S]. For these wavelengths, most of the extinction laws, such as those obtained for the Milky Way [@1976asqu.book.....A; @1986ApJ...307..286F], the Large Magellanic Cloud [@1986ApJ...307..286F], the Small Magellanic Cloud , and starburst galaxies [@2000ApJ...533..682C], agree [see @2019MNRAS.483.2382W]. We adopt a parametrized extinction law from @1989ApJ...345..245C, which depends on two parameters, the total extinction in the $V$-band, $A_V$, and the total-to-selective extinction, $R_V$. The total extinction is modeled according to the prior

$$A_V \sim \textrm{Exponential}(0.2)\text{,}$$

where $0.2$ represents the mean value of the exponential distribution. This prior restricts the value of the extinction to positive values and also favors smaller extinction 