Journal
PHYSICAL REVIEW D
Volume 103, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.103.043508
Keywords
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Funding
- WFIRST program [NNG26PJ30C, NNN12AA01C]
- Simons Foundations Origins of the Universe program
- Corning Glass Works Fellowship
- National Science Foundation [PHY-1820775]
- Canadian Institute for Advanced Research (CIFAR) Program on Gravity and the Extreme Universe
- Simons Foundation Modern Inflationary Cosmology initiative
- Alfred P. Sloan Foundation
- National Science Foundation
- U.S. Department of Energy Office of Science
- University of Arizona
- Brazilian Participation Group
- Brookhaven National Laboratory
- Carnegie Mellon University
- University of Florida
- French Participation Group
- German Participation Group
- Harvard University
- Instituto de Astrofisica de Canarias
- Michigan State/Notre Dame/JINA Participation Group
- Johns Hopkins University
- Lawrence Berkeley National Laboratory
- Max Planck Institute for Astrophysics
- Max Planck Institute for Extraterrestrial Physics
- New Mexico State University
- New York University
- Ohio State University
- Pennsylvania State University
- University of Portsmouth
- Princeton University
- Spanish Participation Group
- University of Tokyo
- University of Utah
- Vanderbilt University
- University of Virginia
- University of Washington
- Yale University
Ask authors/readers for more resources
Creating accurate and low-noise covariance matrices is a challenge in modern cosmology, but a formalism presented in this study compresses observables into a small number of bins by minimizing log-likelihood error in a specific subspace. This leads to significant reduction in noise and allows for accurate parameter inference using fewer mocks. The method is validated with full-shape analyses of power spectra from BOSS DR12 mock catalogs, demonstrating the effectiveness of compressing observables into a lower-dimensional subspace for accurate cosmology studies.
Creating accurate and low-noise covariance matrices represents a formidable challenge in modem-day cosmology. We present a formalism to compress arbitrary observables into a small number of bins by projection into a model-specific subspace that minimizes the prior-averaged log-likelihood error. The lower dimensionality leads to a dramatic reduction in covariance matrix noise, significantly reducing the number of mocks that need to be computed. Given a theory model, a set of priors, and a simple model of the covariance, our method works by using singular value decompositions to construct a basis for the observable that is close to Euclidean; by restricting to the first few basis vectors, we can capture almost all the constraining power in a lower-dimensional subspace. Unlike conventional approaches, the method can be tailored for specific analyses and captures nonlinearities that are not present in the Fisher matrix, ensuring that the full likelihood can be reproduced. The procedure is validated with full-shape analyses of power spectra from Baryon Oscillation Spectroscopic Survey (BOSS) DR12 mock catalogs, showing that the 96-bin power spectra can be replaced by 12 subspace coefficients without biasing the output cosmology; this allows for accurate parameter inference using only similar to 100 mocks. Such decompositions facilitate accurate testing of power spectrum covariances; for the largest BOSS data chunk, we find the following: (a) analytic covariances provide accurate models (with or without trispectrum terms); and (b) using the sample covariance from the MultiDark-Patchy mocks incurs a similar to 0.5 sigma shift in Omega(m) unless the subspace projection is applied. The method is easily extended to higher order statistics; the similar to 2000-bin bispectrum can be compressed into only similar to 10 coefficients, allowing for accurate analyses using few mocks and without having to increase the bin sizes.
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