Cosmological Inference from Galaxy-Clustering Power Spectrum:
  Gaussianization and Covariance Decomposition
  Likelihood fitting to two-point clustering statistics made from galaxy
surveys usually assumes a multivariate normal distribution for the
measurements, with justification based on the central limit theorem given the
large number of overdensity modes. However, this assumption cannot hold on the
largest scales where the number of modes is low. Whilst more accurate
distributions have previously been developed in idealized cases, we derive a
procedure suitable for analysing measured monopole power spectra with window
effects, stochastic shot noise, and the dependence of the covariance matrix on
the model being fitted all taken into account. A data transformation is
proposed to give an approximately Gaussian likelihood, with a
variance--correlation decomposition of the covariance matrix to account for its
cosmological dependence. By comparing with the modified-$t$ likelihood derived
under the usual normality assumption, we find in numerical tests that our new
procedure gives more accurate constraints on the local non-Gaussianity
parameter $f_\mathrm{NL}$, which is sensitive to the large-scale power. A
simple data analysis pipeline is provided for straightforward application of
this new approach in preparation for forthcoming large galaxy surveys such as
DESI and Euclid.
