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We explore two methods of compressing the redshift space galaxy powerspectrum and bispectrum with respect to a chosen set of cosmologicalparameters. Both methods involve reducing the dimension of the originaldata-vector ( e.g. 1000 elements ) to the number of cosmological parametersconsidered ( e.g. seven ) using the Karhunen-Lo\`eve algorithm. In the firstcase, we run MCMC sampling on the compressed data-vector in order to recoverthe one-dimensional (1D) and two-dimensional (2D) posterior distributions. Thesecond option, approximately 2000 times faster, works by orthogonalising theparameter space through diagonalisation of the Fisher information matrix beforethe compression, obtaining the posterior distributions without the need of MCMCsampling. Using these methods for future spectroscopic redshift surveys likeDESI, EUCLID and PFS would drastically reduce the number of simulations neededto compute accurate covariance matrices with minimal loss of constrainingpower. We consider a redshift bin of a DESI-like experiment. Using the powerspectrum combined with the bispectrum as a data-vector, both compressionmethods on average recover the 68% credible regions to within 0.7% and 2% ofthose resulting from standard MCMC sampling respectively. These confidenceintervals are also smaller than the ones obtained using only the power spectrumby (81%, 80%, 82%) respectively for the bias parameter b_1, the growth rate fand the scalar amplitude parameter A_s.

Maximal compression of the redshift space galaxy power spectrum and bispectrum