Debiasing inference with approximate covariance matrices and other unidentified biases

Abstract

When a posterior peaks in unexpected regions of parameter space, new physics has either been discovered, or a bias has not been identified yet. To tell these two cases apart is of paramount importance. We therefore present a method to indicate and mitigate unrecognized biases: Our method runs any pipeline with possibly unknown biases on both simulations and real data. It computes the coverage probability of posteriors, which measures whether posterior volume is a faithful representation of probability or not. If found to be necessary, the posterior is then corrected. This is a non-parametric debiasing procedure which complies with objective Bayesian inference. We use the method to debias inference with approximate covariance matrices and redshift uncertainties. We demonstrate why approximate covariance matrices bias physical constraints, and how this bias can be mitigated. We show that for a Euclid-like survey, if a traditional likelihood exists, then 25 end-to-end simulations suffice to guarantee that the figure of merit deteriorates maximally by 22 percent, or by 10 percent for 225 simulations. Thus, even a pessimistic analysis of Euclid-like data will still constitute an 25-fold increase in precision on the dark energy parameters in comparison to the state of the art (2018) set by KiDS and DES. We provide a public code of our method.

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• Post-Limber Weak Lensing Bispectrum, Reduced Shear Correction, and Magnification Bias Correction
• A new approach to modelling gamma-ray burst afterglows: Using Gaussian processes to account for the systematics
• The impact of braiding covariance and in-survey covariance on next-generation galaxy surveys
• Forecasting constraints on the mean free path of ionizing photons at $z\ge 5.4$ from the Lyman-$\alpha$ forest flux auto-correlation function
• Efficient computation of the super-sample covariance for stage IV galaxy surveys
• Accessing the high-$\ell$ frontier under the Reduced Shear Approximation with $k$-cut Cosmic Shear
• Gaussian Mixture Models for Blended Photometric Redshifts
• Cosmological inference including massive neutrinos from the matter power spectrum: biases induced by uncertainties in the covariance matrix
• On the Robustness of Cluster Clustering Covariance Calibration
• Efficient neutral-IGM inference from noisy 21-cm forest spectra with latent-space U-Net encoding and XGBoost
• Matching Bayesian and frequentist coverage probabilities when using an approximate data covariance matrix