Analytical marginalisation over photometric redshift uncertainties in cosmic shear analyses

As the statistical power of imaging surveys grows, it is crucial to account for all systematic uncertainties. This normally done by constructing a model these uncertainties and then marginalizing over additional parameters. The resulting high dimensionality total parameter spaces makes inferring cosmological parameters significantly more costly using traditional Monte-Carlo sampling methods. A particularly relevant example redshift distribution, $p(z)$, source samples, which may require tens describe fully. However, relatively tight priors can be usually placed on through calibration associated systematics. In this paper we show, quantitatively, that linearisation theoretical prediction with respect calibratable allows us analytically marginalise extra parameters, leading factor $\sim30$ reduction in time needed inference, while accurately recovering same posterior distributions would obtained full numerical marginalisation 160 $p(z)$ We demonstrate feasible not only current data achievable but also future Stage-IV datasets.