Combining high-z galaxy luminosity functions with Bayesian evidence

Galaxy formation during the first billion years of our Universe remains a challenging problem at the forefront of astrophysical cosmology. Although these $z \geq 6$ galaxies are likely responsible for the last major phase change of our Universe, the epoch of reionization (EoR), detailed studies are possible only for relatively rare, bright objects. Characterizing the fainter galaxies which are more representative of the population as a whole is currently done mainly through their non-ionizing UV luminosity function (LF). Observing the faint end of the UV LFs is nevertheless challenging, and current estimates can differ by orders of magnitude. Here we propose a methodology to combine disparate high-$z$ UV LF data sets in a Bayesian framework: Bayesian Data Averaging (BDA). Using a flexible, physically-motivated galaxy model, we compute the relative evidence of various $z=6$ UV LFs within the magnitude range $-20 \leq M_{\rm UV} \leq -15$ which is common to the data sets. Our model, based primarily on power-law scalings of the halo mass function, naturally penalizes systematically jagged data points as well as mis-estimated errors. We then use the relative evidence to weigh the posteriors obtained from disparate LF observations during the EoR, $6 \leq z \leq 10$. The resulting LFs suggest that the star formation rate density (SFRD) integrated down to a UV magnitude of -17 represent $60.9^{+11.3}_{-9.6}\%$ / $28.2^{+9.3}_{-10.1}\%$ / $5.7^{+4.5}_{-4.7}\%$ of the total SFRD at redshifts 6 / 10 / 15. The BDA framework we introduce enables galaxy models to leverage multiple, analogous observational data sets.