Control variates with Zeldovich mocks reduce covariance matrix variance by up to an order of magnitude on large scales in DESI-like mocks.
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Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
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abstract
AIMS. The maximum-likelihood method is the standard approach to obtain model fits to observational data and the corresponding confidence regions. We investigate possible sources of bias in the log-likelihood function and its subsequent analysis, focusing on estimators of the inverse covariance matrix. Furthermore, we study under which circumstances the estimated covariance matrix is invertible. METHODS. We perform Monte-Carlo simulations to investigate the behaviour of estimators for the inverse covariance matrix, depending on the number of independent data sets and the number of variables of the data vectors. RESULTS. We find that the inverse of the maximum-likelihood estimator of the covariance is biased, the amount of bias depending on the ratio of the number of bins (data vector variables), P, to the number of data sets, N. This bias inevitably leads to an -- in extreme cases catastrophic -- underestimation of the size of confidence regions. We report on a method to remove this bias for the idealised case of Gaussian noise and statistically independent data vectors. Moreover, we demonstrate that marginalisation over parameters introduces a bias into the marginalised log-likelihood function. Measures of the sizes of confidence regions suffer from the same problem. Furthermore, we give an analytic proof for the fact that the estimated covariance matrix is singular if P>N.
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astro-ph.CO 16representative citing papers
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Using idealized synthetic data, knowing the true continuum in Lyα forest auto- and cross-correlations reduces uncertainties on the AP parameter and Ω_m by ~10%, with extension to 240 h^{-1}Mpc scales adding up to ~15% further improvement equivalent to a 40% larger survey area.
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Joint kSZ-clustering analysis of ACT DR6 and CMASS yields a halo optical depth profile more extended than Websky simulations, suggesting stronger baryonic feedback.
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Fixing the covariance at an incorrect cosmology in cluster count analyses leaves Ω_c, σ_8, and w estimates unbiased but distorts their uncertainties, driven by S_8 amplitude effects; a single update at the recovered best-fit cosmology restores correct normalization for LSST-like surveys.
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DESI 2024 V: Full-Shape Galaxy Clustering from Galaxies and Quasars
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Cosmology-dependent covariance in galaxy cluster number counts: consequences for parameter inference
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Revisiting the 'Lensing is Low' Problem with UNIONS
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Counting voids and filaments: Betti Curves as a Powerful Probe for Cosmology
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Constraints on primordial non-Gaussianity from Quaia
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