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

Understand

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.