Dark energy survey internal consistency tests of the joint cosmological probes analysis with posterior predictive distributions

Abstract

Beyond-ΛCDM physics or systematic errors may cause subsets of a cosmological data set to appear inconsistent when analyzed assuming ΛCDM. 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 ΛCDM. We find that the DES Y1 data have an acceptable goodness of fit to ΛCDM, 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.

Dark Energy Survey Year 3 results: Cosmology from cosmic shear and robustness to data calibration

“…We demonstrate that the cosmology is insensitive to an additional, unaccounted for shear uncertainty. (iii) We evaluate the internal consistency of the cosmicshear measurements using a PPD method [114]. We find all p-values to pass our threshold and at the analysis level we find the S 8 posteriors to be consistent across small and large scales, low and high redshift and between two-point shear statistics to ∼1σ, which serves as a useful validation of some scale-dependent, or redshift-dependent, unaccounted for uncertainty.…”

“…For tests in data space, the Posterior Predictive Distribution (PPD) methodology detailed in Ref. [114] is used. We consider two types of internal consistency tests: goodness of fit tests, and consistency tests.…”

“…In this case, Pðd 0 sim jd obs ; pÞ is the conditional likelihood, that is, the distribution of d 0 sim at parameters p given observations for d obs . Here a multivariate Gaussian likelihood is assumed, so the conditional likelihood is also multivariate Gaussian, with shifted mean and covariance accounting for the correlation between the subsets d and d 0 (see [114] for details). To perform the comparison of the results, a statistic is defined to compare PPD realizations and observations of d 0 , integrated over parameter space.…”

“…For this, χ 2 ðd 0 ; pÞ is used, defined with respect to the model at parameters p. This statistic determines the statistical significance of consistency through a p-value, which is given by the fraction of parameter samples p for which χ 2 ðd 0 sim ; pÞ > χ 2 ðd 0 obs ; pÞ. As demonstrated in [114], this choice of test statistic may yield overly conservative p-values, especially in the case where parameter posteriors from d and d 0 are very different. For this reason, a calibration procedure is followed as outlined there, based on repeated tests for simulated data vectors consistently drawn at the fiducial cosmology.…”

“…(iv) The general methodology, likelihood analysis and covariance used in the cosmological analyses shown in this work and the DES Collaboration [104] is presented in Krause et al [111] and Friedrich et al [112], and this methodology is independently validated using realistic simulations in DeRose et al [113]. (v) The statistical framework to assess the internal consistency of the DES data and measurements is presented in Doux et al [114] and the consistency with independent, external data in Lemos et al [115]. This paper is structured as follows: in Secs.…”