Photometric redshifts for future cosmological galaxy surveys

Photometric galaxy surveys are a very useful probe that can place constraints on cosmological parameters and test the cosmological model. Future galaxy surveys such as the Large Synoptic Survey Telescope (LSST) will increase the precision of their constraints by observing to fainter magnitudes than previous surveys. While the increased depth of these future surveys will produce higher precision constraints, it will also increase the fraction of sources that overlap with other sources along the line of sight, known as blending. Current methods for dealing with these blended sources involve deblending, separating images of sources into their individual constituents. While this enables their analysis using existing methods designed for unblended sources, this separation makes quantifying and propagating all uncertainties difficult. This thesis presents a different approach, applied to the problem of photometric redshifts. By constructing photometric redshift methods that can infer the redshifts of sources directly from blended data, the associated uncertainties can be easily quantified, a vital step for ensuring the final cosmological constraints of galaxy surveys represent an accurate reflection of our state of knowledge. We first generalise existing Bayesian template-based photometric redshift methods to the case of blended sources. By performing parameter inference on the resulting model, we obtain joint posterior distributions of the redshifts of all constituents within a blended source, completely describing all correlations between these quantities. We then cast the problem of identifying the number of constituents within a blended source as a model comparison problem. Next, we develop a machine learning-based photometric redshift method that can infer the redshifts of sources after being trained on a training set of unblended sources. By using a Gaussian mixture model to do this, the posterior distributions and Bayesian evidences necessary for model comparison can be computed efficiently, enabling the method to be applied to large datasets. Finally, we develop two Bayesian hierarchical models that can infer posterior distributions over redshift distributions of a population of possibly blended sources. We do this by constructing three Gaussian mixture models that share means and covariances but differ in their weights. We test these models using both exact and approximate inference methods. Finally, we conclude by suggesting several possible extensions to this work.