The DESI PRObabilistic Value-Added Bright Galaxy Survey (PROVABGS) Mock Challenge

The PRObabilistic Value-Added Bright Galaxy Survey (PROVABGS) catalog will provide measurements of galaxy properties, such as stellar mass ($M_*$), star formation rate (${\rm SFR}$), stellar metallicity ($Z_{\rm MW}$), and stellar age ($t_{\rm age, MW}$), for >10 million galaxies of the DESI Bright Galaxy Survey. Full posterior distributions of the galaxy properties will be inferred using state-of-the-art Bayesian spectral energy distribution (SED) modeling of DESI spectroscopy and Legacy Surveys photometry. In this work, we present the SED model, Bayesian inference framework, and methodology of PROVABGS. Furthermore, we apply the PROVABGS SED modeling on realistic synthetic DESI spectra and photometry, constructed using the L-GALAXIES semi-analytic model. We compare the inferred galaxy properties to the true galaxy properties of the simulation using a hierarchical Bayesian framework to quantify accuracy and precision. Overall, we accurately infer the true $M_*$, ${\rm SFR}$, $Z_{\rm MW}$, and $t_{\rm age, MW}$ of the simulated galaxies. However, the priors on galaxy properties induced by the SED model have a significant impact on the posteriors. They impose a ${\rm SFR}{>}10^{-1} M_\odot/{\rm yr}$ lower bound on ${\rm SFR}$, a ${\sim}0.3$ dex bias on $\log Z_{\rm MW}$ for galaxies with low spectral signal-to-noise, and $t_{\rm age, MW} < 8\,{\rm Gyr}$ upper bound on stellar age. This work also demonstrates that a joint analysis of spectra and photometry significantly improves the constraints on galaxy properties over photometry alone and is necessary to mitigate the impact of the priors. With the methodology presented and validated in this work, PROVABGS will maximize information extracted from DESI observations and provide a probabilistic value-added galaxy catalog that will extend current galaxy studies to new regimes and unlock cutting-edge probabilistic analyses.