# Debiasing inference with approximate covariance matrices and other unidentified biases

## TL;DR

The paper introduces a non-parametric, objective Bayesian method to detect and correct biases in posterior inferences, especially those caused by approximate covariance matrices, demonstrated on Euclid-like survey data.

## Contribution

It presents a novel bias detection and correction technique that assesses posterior coverage and applies debiasing, improving inference reliability in cosmological analyses.

## Key findings

- Approximate covariance matrices bias physical constraints.
- Debiasing reduces bias impact on parameter estimation.
- Method improves precision in dark energy parameters.

## 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.