Conservative cosmology: combining data with allowance for unknown systematics

TL;DR

This paper introduces BACCUS, a Bayesian method for combining cosmological data sets that accounts for unknown systematic biases, providing more reliable parameter estimates amid conflicting experiments.

Contribution

The paper presents a novel hyperparameter-based approach, BACCUS, that conservatively incorporates unknown systematics into cosmological data analysis, improving robustness over existing methods.

Findings

BACCUS effectively models unknown systematics in cosmological data.

The method reveals extended tails in posterior distributions due to large potential shifts.

Application to the H0 tension demonstrates the approach's ability to handle conflicting data.

Abstract

When combining data sets to perform parameter inference, the results will be unreliable if there are unknown systematics in data or models. Here we introduce a flexible methodology, BACCUS: BAyesian Conservative Constraints and Unknown Systematics, which deals in a conservative way with the problem of data combination, for any degree of tension between experiments. We introduce hyperparameters that describe a bias in each model parameter for each class of experiments. A conservative posterior for the model parameters is then obtained by marginalization both over these unknown shifts and over the width of their prior. We contrast this approach with an existing hyperparameter method in which each individual likelihood is scaled, comparing the performance of each approach and their combination in application to some idealized models. Using only these rescaling hyperparameters is not a suitable approach for the current observational situation, in which internal null tests of the errors are passed, and yet different experiments prefer models that are in poor agreement. The possible existence of large shift systematics cannot be constrained with a small number of data sets, leading to extended tails on the conservative posterior distributions. We illustrate our method with the case of the $H_0$ tension between results from the cosmic distance ladder and physical measurements that rely on the standard cosmological model.