Dark Energy Survey internal consistency tests of the joint cosmological probes analysis with posterior predictive distributions

Beyond-$Lambda$CDM physics or systematic errors may cause subsets of a cosmological data set to appear inconsistent when analyzed assuming $Lambda$CDM. We present an application of internal consistency tests to measurements from the Dark Energy Survey Year 1 (DES Y1) joint probes analysis. Our analysis relies on computing the posterior predictive distribution (PPD) for these data under the assumption of $Lambda$CDM. We find that the DES Y1 data have an acceptable goodness of fit to $Lambda$CDM, with a probability of finding a worse fit by random chance of ${p = 0.046}$. Using numerical PPD tests, supplemented by graphical checks, we show that most of the data vector appears completely consistent with expectations, although we observe a small tension between large- and small-scale measurements. A small part (roughly 1.5%) of the data vector shows an unusually large departure from expectations; excluding this part of the data has negligible impact on cosmological constraints, but does significantly improve the $p$-value to 0.10. The methodology developed here will be applied to test the consistency of DES Year 3 joint probes data sets....