Bayesian evidence as a tool for comparing datasets

Abstract

We introduce a new conservative test for quantifying the consistency of two or more datasets. The test is based on the Bayesian answer to the question, ``How much more probable is it that all my data were generated from the same model system than if each dataset were generated from an independent set of model parameters?''. We make explicit the connection between evidence ratios and the differences in peak chi-squared values, the latter of which are more widely used and more cheaply calculated. Calculating evidence ratios for three cosmological datasets (recent CMB data (WMAP, ACBAR, CBI, VSA), SDSS and the most recent SNe Type 1A data) we find that concordance is favoured and the tightening of constraints on cosmological parameters is indeed justified.