The full Fisher matrix for galaxy surveys
  Starting from the Fisher matrix for counts in cells, I derive the full Fisher
matrix for surveys of multiple tracers of large-scale structure. The key
assumption is that the inverse of the covariance of the galaxy counts is given
by the naive matrix inverse of the covariance in a mixed position-space and
Fourier-space basis. I then compute the Fisher matrix for the power spectrum in
bins of the three-dimensional wavenumber k; the Fisher matrix for functions of
position x (or redshift z) such as the linear bias of the tracers and/or the
growth function; and the cross-terms of the Fisher matrix that expresses the
correlations between estimations of the power spectrum and estimations of the
bias. When the bias and growth function are fully specified, and the
Fourier-space bins are large enough that the covariance between them can be
neglected, the Fisher matrix for the power spectrum reduces to the widely used
result that was first derived by Feldman, Kaiser and Peacock (1994). Assuming
isotropy, an exact calculation of the Fisher matrix can be performed in the
case of a constant-density, volume-limited survey. I then show how the exact
Fisher matrix in the general case can be obtained in terms of a series of
volume-limited surveys.
