Photometric Redshift Uncertainties in Weak Gravitational Lensing Shear Analysis: Models and Marginalization

Recovering credible cosmological parameter constraints in a weak lensing shear analysis requires an accurate model that can be used to marginalize over nuisance parameters describing potential sources of systematic uncertainty, such as the uncertainties on the sample redshift distribution $n(z)$. Due to the challenge of running Markov Chain Monte-Carlo (MCMC) in the high dimensional parameter spaces in which the $n(z)$ uncertainties may be parameterized, it is common practice to simplify the $n(z)$ parameterization or combine MCMC chains that each have a fixed $n(z)$ resampled from the $n(z)$ uncertainties. In this work, we propose a statistically-principled Bayesian resampling approach for marginalizing over the $n(z)$ uncertainty using multiple MCMC chains. We self-consistently compare the new method to existing ones from the literature in the context of a forecasted cosmic shear analysis for the HSC three-year shape catalog, and find that these methods recover similar cosmological parameter constraints, implying that using the most computationally efficient of the approaches is appropriate. However, we find that for datasets with the constraining power of the full HSC survey dataset (and, by implication, those upcoming surveys with even tighter constraints), the choice of method for marginalizing over $n(z)$ uncertainty among the several methods from the literature may significantly impact the statistical uncertainties on cosmological parameters, and a careful model selection is needed to ensure credible parameter intervals.