Improving Fisher matrix forecasts for galaxy surveys: window function,
  bin cross-correlation, and bin redshift uncertainty
  The Fisher matrix is a widely used tool to forecast the performance of future
experiments and approximate the likelihood of large data sets. Most of the
forecasts for cosmological parameters in galaxy clustering studies rely on the
Fisher matrix approach for large-scale experiments like DES, Euclid, or SKA.
Here we improve upon the standard method by taking into account three effects:
the finite window function, the correlation between redshift bins, and the
uncertainty on the bin redshift. The first two effects are negligible only in
the limit of infinite surveys. The third effect, on the contrary, is negligible
for infinitely small bins. Here we show how to take into account these effects
and what the impact on forecasts of a Euclid-type experiment will be. The main
result of this article is that the windowing and the bin cross-correlation
induce a considerable change in the forecasted errors, of the order of 10-30%
for most cosmological parameters, while the redshift bin uncertainty can be
neglected for bins smaller than $\Delta z = 0.1$ roughly.
