A Joint Analysis for Cosmology and Photometric Redshift Calculation
  Using Cross Correlations
  We present a method of calibrating the properties of photometric redshift
bins as part of a larger Markov Chain Monte Carlo (MCMC) analysis for the
inference of cosmological parameters. The redshift bins are characterised by
their mean and variance, which are varied as free parameters and marginalised
over when obtaining the cosmological parameters. We demonstrate that the
likelihood function for cross-correlations in an angular power spectrum
framework tightly constrains the properties of bins such that they may be well
determined, reducing their influence on cosmological parameters and avoiding
the bias from poorly estimated redshift distributions. We demonstrate that even
with only three photometric and three spectroscopic bins, we can recover
accurate estimates of the mean redshift of a bin to within $\Delta\mu \approx
3-4 \times10^{-3}$ and the width of the bin to $\Delta\sigma \approx
1\times10^{-3}$ for galaxies near $z = 1$. This indicates that we may be able
to bring down the photometric redshift errors to a level which is in line with
the requirements for the next generation of cosmological experiments.
