Therefore, we use a Bayesian statistical model to fit the of the galaxies and to estimate the stellar population parameters. Using this approach, we can identify possible parameter correlations and provide uncertainties that are marginalized over the distribution of all the other parameters in the model.

Bayes’ theorem allows for the inference of the probability distribution of a set of parameters $\theta$ in a statistical model based on a dataset $D$ using the relation

$$p(\theta | D) \propto p(\theta) p(D|\theta)\text{,}$$

where $p(\theta|D)$ represents the posterior probability distribution of the parameters $\theta$ given the data $D$, $p(\theta)$ represents the prior distribution of the parameters, and $p(D|\theta)$ is the likelihood distribution [see, e.g. @gelmanbda04]. Below we describe the priors for all of the parameters in our model.

Prior and likelihood distributions
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The flux scale factor $f_0$ can vary by orders of magnitude depending on the brightness of the source. Therefore, it is more convenient to model its logarithm, which can be described by the prior

$$\log f_0 \sim \textrm{Normal}(\mu_{0}, \sigma_{0}^2)\text{,}$$

where $\mu_{0}$ and $\sigma_{0}^2$ indicate the mean and the variance of the distribution respectively. In practice, we estimate $\mu_{0}$ using the data, and we assume $\sigma_{0}=3$ to allow a large range 