values rather than large. We also allow $R_V$ to vary in our models using the prior

$$R_V \sim \textrm{Normal}^+(3.1, 1.)\mbox{,}$$

which assumes that the total-to-selective extinction is similar to that measured generally within the Milky Way . The plus signal indicates that we restrict $R_V$ to positive values.

Finally, it is necessary to define a log-likelihood for the use of the Bayes’ theorem. The widely common assumption is that the observed consists of independent, normal random variables, and thus the log-likelihood can be simply described as a $\chi^2$-distribution. However, the accuracy of the model determined using the normal assumption may be compromised if the observations contain outliers [see @Vanhatalo2009]. In observational settings, the causes of outliers may be either external to the source, such as contamination by cosmic rays or the incomplete removal of sky, or internal to the source, as is the case when the model is incomplete, for example when it does not account for emission lines.

Emission lines have been directly observed in optical observations of at least one cluster UDG [@2017ApJ...838L..21K], and may be common in field UDGs [@2017ApJ...842..133L]. Observationally, emission lines systematically inflate the observed fluxes in passbands in which they appear, an effect that 