A Bayesian Hierarchical Model for Photometric Redshifts

The Sloan Digital Sky Survey (SDSS) is an extremely large astronomical survey conducted with the intention of mapping more than a quarter of the sky (http://www.sdss.org/). Among the data it is generating are spectroscopic and photometric measurements, both allowing estimation of the redshift of galaxies. The former is precise but expensive to gather, the latter is far cheaper but correspondingly gives far less accurate estimates. A recent paper by Csabai et al. (2003) describes various calibration techniques aiming to predict spectroscopic redshift from photometric measurements. In this paper, we investigate what a structured Bayesian approach to the problem can add. In particular, we are interested in providing uncertainty bounds associated with the underlying redshifts and the classifications of the galaxies. We find that a quite generic statistical modelling approach, using for the most part standard model ingredients, can compete with much more specific custom-made and highly-tuned techniques already available in the astronomical literature.