A Bayesian Approach to Calibrating Period-Luminosity Relations of RR
  Lyrae Stars in the Mid-Infrared
  A Bayesian approach to calibrating period-luminosity (PL) relations has
substantial benefits over generic least-squares fits. In particular, the
Bayesian approach takes into account the full prior distribution of the model
parameters, such as the a priori distances, and refits these parameters as part
of the process of settling on the most highly-constrained final fit.
Additionally, the Bayesian approach can naturally ingest data from multiple
wavebands and simultaneously fit the parameters of PL relations for each
waveband in a procedure that constrains the parameter posterior distributions
so as to minimize the scatter of the final fits appropriately in all wavebands.
Here we describe the generalized approach to Bayesian model fitting and then
specialize to a detailed description of applying Bayesian linear model fitting
to the mid-infrared PL relations of RR Lyrae variable stars. For this example
application we quantify the improvement afforded by using a Bayesian model fit.
We also compare distances previously predicted in our example application to
recently published parallax distances measured with the Hubble Space Telescope
and find their agreement to be a vindication of our methodology. Our intent
with this article is to spread awareness of the benefits and applicability of
this Bayesian approach and encourage future PL relation investigations to
consider employing this powerful analysis method.
