Massive data compression for parameter-dependent covariance matrices
  We show how the massive data compression algorithm MOPED can be used to
reduce, by orders of magnitude, the number of simulated datasets that are
required to estimate the covariance matrix required for the analysis of
gaussian-distributed data. This is relevant when the covariance matrix cannot
be calculated directly. The compression is especially valuable when the
covariance matrix varies with the model parameters. In this case, it may be
prohibitively expensive to run enough simulations to estimate the full
covariance matrix throughout the parameter space. This compression may be
particularly valuable for the next-generation of weak lensing surveys, such as
proposed for Euclid and LSST, for which the number of summary data (such as
band power or shear correlation estimates) is very large, $\sim 10^4$, due to
the large number of tomographic redshift bins that the data will be divided
into. In the pessimistic case where the covariance matrix is estimated
separately for all points in an MCMC analysis, this may require an unfeasible
$10^9$ simulations. We show here that MOPED can reduce this number by a factor
of 1000, or a factor of $\sim 10^6$ if some regularity in the covariance matrix
is assumed, reducing the number of simulations required to a manageable $10^3$,
making an otherwise intractable analysis feasible.
