The statistical properties of a map of the primary fluctuations in the cosmic
microwave background (CMB) may be specified to high accuracy by a few thousand
power spectra measurements, provided the fluctuations are gaussian, yet the
number of parameters relevant for the CMB is probably no more than about 10-20.
There is consequently a large degree of redundancy in the power spectrum data.
In this paper, we show that the MOPED data compression technique can reduce the
CMB power spectrum measurements to about 10-20 numbers (one for each
parameter), from which the cosmological parameters can be estimated virtually
as accurately as from the complete power spectrum. This offers opportunities
for very fast parameter estimation from real and simulated CMB skies, with
accurate likelihood calculations at Planck resolution being speeded up by a
factor of around five hundred million.Comment: version to appear in MNRA