Objective Bayesian analysis of neutrino masses and hierarchy

Given the precision of current neutrino data, priors still impact noticeably the constraints on neutrino masses and their hierarchy. To avoid our understanding of neutrinos being driven by prior assumptions, we construct a prior that is mathematically minimally informative. Using the constructed uninformative prior, we find that the normal hierarchy is favoured but with inconclusive posterior odds of 5.1:1. Better data is hence needed before the neutrino masses and their hierarchy can be well constrained. We find that the next decade of cosmological data should provide conclusive evidence if the normal hierarchy with negligible minimum mass is correct, and if the uncertainty in the sum of neutrino masses drops below 0.025 eV. On the other hand, if neutrinos obey the inverted hierarchy, achieving strong evidence will be difficult with the same uncertainties. Our uninformative prior was constructed from principles of the Objective Bayesian approach. The prior is called a reference prior and is minimally informative in the specific sense that the information gain after collection of data is maximised. The prior is computed for the combination of neutrino oscillation data and cosmological data and still applies if the data improve.Comment: 15 pages. Minor changes to match accepted version in JCA

On the insufficiency of arbitrarily precise covariance matrices: non-Gaussian weak lensing likelihoods

We investigate whether a Gaussian likelihood, as routinely assumed in the analysis of cosmological data, is supported by simulated survey data. We define test statistics, based on a novel method that first destroys Gaussian correlations in a dataset, and then measures the non-Gaussian correlations that remain. This procedure flags pairs of datapoints which depend on each other in a non-Gaussian fashion, and thereby identifies where the assumption of a Gaussian likelihood breaks down. Using this diagnostic, we find that non-Gaussian correlations in the CFHTLenS cosmic shear correlation functions are significant. With a simple exclusion of the most contaminated datapoints, the posterior for $s_8$ is shifted without broadening, but we find no significant reduction in the tension with $s_8$ derived from Planck Cosmic Microwave Background data. However, we also show that the one-point distributions of the correlation statistics are noticeably skewed, such that sound weak lensing data sets are intrinsically likely to lead to a systematically low lensing amplitude being inferred. The detected non-Gaussianities get larger with increasing angular scale such that for future wide-angle surveys such as Euclid or LSST, with their very small statistical errors, the large-scale modes are expected to be increasingly affected. The shifts in posteriors may then not be negligible and we recommend that these diagnostic tests be run as part of future analyses.Comment: Replacement to match accepted MNRAS versio

Recovering galaxy star formation and metallicity histories from spectra using VESPA

We introduce VErsatile SPectral Analysis (VESPA): a new method which aims to recover robust star formation and metallicity histories from galactic spectra. VESPA uses the full spectral range to construct a galaxy history from synthetic models. We investigate the use of an adaptative parametrization grid to recover reliable star formation histories on a galaxy-by-galaxy basis. Our goal is robustness as opposed to high resolution histories, and the method is designed to return high time resolution only where the data demand it. In this paper we detail the method and we present our findings when we apply VESPA to synthetic and real Sloan Digital Sky Survey (SDSS) spectroscopic data. We show that the number of parameters that can be recovered from a spectrum depends strongly on the signal-to-noise, wavelength coverage and presence or absence of a young population. For a typical SDSS sample of galaxies, we can normally recover between 2 to 5 stellar populations. We find very good agreement between VESPA and our previous analysis of the SDSS sample with MOPED.Comment: In press MNRAS, minor revisions to match accepted version by the journa