Paper: BayeSED-GALAXIES. I. Performance Test for Simultaneous Photometric Redshift and Stellar Population Parameter Estimation of Galaxies in the CSST Wide-field Multiband Imaging Survey
Authors: Yunkun Han, Lulu Fan, Xian Zhong Zheng, Jin-Ming Bai, Zhanwen Han
Figure caption: The Bayesian evidence (BE), maximum likelihood (ML), and metrics of photometric redshift (red cross), stellar mass (blue square), and SFR (green circle) estimation from the Bayesian analysis of the hydrodynamical simulation–based mock galaxy sample for a CSST-like survey employing six SED models (0: SFH = τ, –CEH, DAL = Cal+18; 1: SFH = τ, +CEH, DAL = Cal+18; 2: SFH = τ, +CEH, DAL = Sal+18; 3: SFH = β-τ, +CEH, DAL = Sal+18; 4: SFH = β-τ-r, +CEH, DAL = Sal+18; 5: SFH = α-β-τ-r, +CEH, DAL = Sal+18) with increasing complexity in the forms of SFH and DAL, as well as for cases with (bottom panels) and without noise (top panels). In the case without noise, the simplest model “SFH = τ, –CEH, DAL = Cal+18” has the lowest Bayesian evidence of ﹩\mathrm{ln}(\mathrm{BE})=-88\text{,}042\pm 5936﹩. Meanwhile, the SED models “SFH = τ, +CEH, DAL = Sal+18” and “SFH = β-τ, +CEH, DAL = Sal+18,” which are neither the simplest nor the most complex models, have the largest Bayesian evidences of ﹩\mathrm{ln}(\mathrm{BE})=58\text{,}878\pm 5823﹩ and ﹩\mathrm{ln}(\mathrm{BE})=56\text{,}343\pm 5780,﹩ which are comparable within error bars. Interestingly, the same two models give the highest-quality parameter estimates. It is worth mentioning that the model selection with the maximum likelihood (or equivalently the minimum χ 2) leads to similar results. In contrast to the case without noise, in the case with noise, the two simplest SED models “SFH = τ, –CEH, DAL = Cal+00” and “SFH = τ, +CEH, DAL = Cal+00” have the largest Bayesian evidences of ﹩\mathrm{ln}(\mathrm{BE})=-18\text{,}871\pm 2649﹩ and ﹩\mathrm{ln}(\mathrm{BE})=-18\text{,}661\pm 2649﹩, which are comparable within error bars. It is very interesting that the model selection with the maximum likelihood (or equivalently the minimum χ 2) leads to exactly the opposite results, where the more complex (or flexible) models are always more favored. Similar to the case without noise, the two simplest SED models also give the highest-quality parameter estimates. For photometric redshift, stellar mass, and SFR, accurate estimation becomes increasingly difficult, with the latter two being more sensitive to the selection of SED models. Generally, the quality of parameter estimates is closely related to the level of Bayesian evidence, which is especially clear in the more realistic case with noise. Actually, the quality of parameter estimation, especially that of stellar mass and SFR estimation, significantly decreases with the increase of SED model complexity, which is similar to the case with perfect SED modeling as shown in Figures 4–6, and should be caused by more severe parameter degeneracies suffered by the more flexible SED model. It is clear that, in the more realistic case with noise, the model selection with the maximum likelihood (or equivalently the minimum χ 2) is not consistent with the measurements of the quality of parameter estimation. Since direct measurements of metrics such as NMAD, BIA, and OLF are usually unavailable, Bayesian model comparison with Bayesian evidence can be used to find the best SED model that is not only the most efficient but also gives the best parameter estimation.