42 research outputs found
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 is shifted without broadening, but we find no
significant reduction in the tension with 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
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
A blinding solution for inference from astronomical data
This paper presents a joint blinding and deblinding strategy for inference of
physical laws from astronomical data. The strategy allows for up to three
blinding stages, where the data may be blinded, the computations of theoretical
physics may be blinded, and --assuming Gaussianly distributed data-- the
covariance matrix may be blinded. We found covariance blinding to be
particularly effective, as it enables the blinder to determine close to exactly
where the blinded posterior will peak. Accordingly, we present an algorithm
which induces posterior shifts in predetermined directions by hiding
untraceable biases in a covariance matrix. The associated deblinding takes the
form of a numerically lightweight post-processing step, where the blinded
posterior is multiplied with deblinding weights. We illustrate the blinding
strategy for cosmic shear from KiDS-450, and show that even though there is no
direct evidence of the KiDS-450 covariance matrix being biased, the famous
cosmic shear tension with Planck could easily be induced by a
mischaracterization of correlations between at the highest redshift and
all lower redshifts. The blinding algorithm illustrates the increasing
importance of accurate uncertainty assessment in astronomical inferences, as
otherwise involuntary blinding through biases occurs
Bayesian error propagation for neural-net based parameter inference
Neural nets have become popular to accelerate parameter inferences,
especially for the upcoming generation of galaxy surveys in cosmology. As
neural nets are approximative by nature, a recurrent question has been how to
propagate the neural net's approximation error, in order to avoid biases in the
parameter inference. We present a Bayesian solution to propagating a neural
net's approximation error and thereby debiasing parameter inference. We exploit
that a neural net reports its approximation errors during the validation phase.
We capture the thus reported approximation errors via the highest-order summary
statistics, allowing us to eliminate the neural net's bias during inference,
and propagating its uncertainties. We demonstrate that our method is quickly
implemented and successfully infers parameters even for strongly biased neural
nets. In summary, our method provides the missing element to judge the accuracy
of a posterior if it cannot be computed based on an infinitely accurately
theory code.Comment: 7 pages, 9 figures. Accepted by the Open Journal of Astrophysic