Quantifying Suspiciousness Within Correlated Data Sets

TL;DR

This paper introduces a Bayesian method to quantify tension between correlated datasets, providing a robust diagnostic tool for internal consistency in cosmological surveys, especially when datasets are highly correlated.

Contribution

It extends the Suspiciousness statistic to correlated data with uninformative priors, enabling internal consistency diagnostics using global summary statistics.

Findings

Successfully tested on KiDS-450 data for internal consistency.

Recovered controlled discrepancies in simulated data.

Proposed as a diagnostic for current and future surveys like LSST and Euclid.

Abstract

We propose a principled Bayesian method for quantifying tension between correlated datasets with wide uninformative parameter priors. This is achieved by extending the Suspiciousness statistic, which is insensitive to priors. Our method uses global summary statistics, and as such it can be used as a diagnostic for internal consistency. We show how our approach can be combined with methods that use parameter space and data space to identify the existing internal discrepancies. As an example, we use it to test the internal consistency of the KiDS-450 data in 4 photometric redshift bins, and to recover controlled internal discrepancies in simulated KiDS data. We propose this as a diagnostic of internal consistency for present and future cosmological surveys, and as a tension metric for data sets that have non-negligible correlation, such as LSST and Euclid.