Fewer mocks and less noise: Reducing the dimensionality of cosmological observables with subspace projections

Creating accurate and low-noise covariance matrices represents a formidable challenge in modern-day cosmology. We present formalism to compress arbitrary observables into small number of bins by projection model-specific subspace that minimizes the prior-averaged log-likelihood error. The lower dimensionality leads dramatic reduction matrix noise, significantly reducing mocks need be computed. Given theory model, set priors, simple model covariance, our method works using singular value decompositions construct basis for observable is close Euclidean; restricting first few vectors, we can capture almost all constraining power lower-dimensional subspace. Unlike conventional approaches, tailored specific analyses captures non-linearities are not Fisher matrix, ensuring full likelihood reproduced. procedure validated with full-shape spectra from BOSS DR12 mock catalogs, showing 96-bin replaced 12 coefficients without biasing output cosmology; this allows parameter inference only $\sim 100$ mocks. Such facilitate testing spectrum covariances; largest data chunk, find that: (a) analytic covariances provide models (with or trispectrum terms); (b) sample MultiDark-Patchy incurs 0.5\sigma$ shift $\Omega_m$, unless applied. easily extended higher order statistics; 2000$-bin bispectrum compressed 10$ coefficients, allowing having increase bin sizes.