We provide a new interpretation for the Bayes factor combination used in the Dark Energy Survey (DES) first year analysis to quantify the tension between the DES and Planck datasets. The ratio ...quantifies a Bayesian confidence in our ability to combine the datasets. This interpretation is prior dependent, with wider prior widths boosting the confidence. We therefore propose that if there are any reasonable priors which reduce the confidence to below unity, then we cannot assert that the datasets are compatible. Computing the evidence ratios for the DES first year analysis and Planck, given that narrower priors drop the confidence to below unity, we conclude that DES and Planck are, in a Bayesian sense, incompatible under ΛCDM. Additionally we compute ratios which confirm the consensus that measurements of the acoustic scale by the Baryon Oscillation Spectroscopic Survey (BOSS) are compatible with Planck, while direct measurements of the acceleration rate of the Universe by the Supernovae and H0 for the Equation of State of Dark Energy Collaboration (SH0ES) are not. We propose a modification to the Bayes ratio which removes the prior dependency using Kullback-Leibler divergences, and using this statistical test we find Planck in strong tension with SH0ES, in moderate tension with DES, and in no tension with BOSS. We propose this statistic as the optimal way to compare datasets, ahead of the next DES data releases, as well as future surveys. Finally, as an element of these calculations, we introduce in a cosmological setting the Bayesian model dimensionality, which is a parametrization-independent measure of the number of parameters that a given dataset constrains.
The curvature parameter tension between Planck 2018, cosmic microwave background (CMB) lensing, and baryon acoustic oscillation (BAO) data is measured using the suspiciousness statistic to be 2.5–3s. ...Conclusions regarding the spatial curvature of the Universe which stem from the combination of these data should therefore be viewed with suspicion. Without CMB lensing or BAO, Planck 2018 has a moderate preference for closed universes, with Bayesian betting odds of over 50 : 1 against a flat universe and over 2000 : 1 against an open universe.
Exact numerical primordial primordial power spectra are computed and plotted for the best-fit Planck 2018 curved universe parameters. It is found that the spectra have generic cutoffs and ...oscillations within the observable window for the level of curvature allowed by current cosmic microwave background measurements and provide a better fit to current data. Derivations for the Mukhanov-Sasaki equation for curved universes are presented and analyzed, and theoretical implications for the quantum and classical initial conditions for inflation are discussed within the curved regime.
ABSTRACT
We propose a principled Bayesian method for quantifying tension between correlated data sets with wide uninformative parameter priors. This is achieved by extending the Suspiciousness ...statistic, which is insensitive to priors. Our method uses global summary statistics, and as such it can be used as a diagnostic for internal consistency. We show how our approach can be combined with methods that use parameter space and data space to identify the existing internal discrepancies. As an example, we use it to test the internal consistency of the KiDS-450 data in four photometric redshift bins, and to recover controlled internal discrepancies in simulated KiDS data. We propose this as a diagnostic of internal consistency for present and future cosmological surveys, and as a tension metric for data sets that have non-negligible correlation, such as Large Synoptic Spectroscopic Survey and Euclid.
We present three nonparametric Bayesian primordial reconstructions using Planck 2018 polarization data: linear spline primordial power spectrum reconstructions, cubic spline inflationary potential ...reconstructions, and sharp-featured primordial power spectrum reconstructions. All three methods conditionally show hints of an oscillatory feature in the primordial power spectrum in the multipole range ℓ∼20 to ℓ∼50, which is to some extent preserved upon marginalization. We find no evidence for deviations from a pure power law across a broad observable window (50≲ℓ≲2000), but find that parametrizations are preferred which are able to account for lack of resolution at large angular scales due to cosmic variance, and at small angular scales due to Planck instrument noise. Furthermore, the late-time cosmological parameters are unperturbed by these extensions to the primordial power spectrum. This work is intended to provide a background and give more details of the Bayesian primordial reconstruction work found in the Planck 2018 papers.
Exploring phase space with nested sampling Yallup, David; Janßen, Timo; Schumann, Steffen ...
European physical journal. C, Particles and fields,
08/2022, Volume:
82, Issue:
8
Journal Article
Peer reviewed
Open access
We present the first application of a Nested Sampling algorithm to explore the high-dimensional phase space of particle collision events. We describe the adaptation of the algorithm, designed to ...perform Bayesian inference computations, to the integration of partonic scattering cross sections and the generation of individual events distributed according to the corresponding squared matrix element. As a first concrete example we consider gluon scattering processes into 3-, 4- and 5-gluon final states and compare the performance with established sampling techniques. Starting from a flat prior distribution Nested Sampling outperforms the
Vegas
algorithm and achieves results comparable to a dedicated multi-channel importance sampler. We outline possible approaches to combine Nested Sampling with non-flat prior distributions to further reduce the variance of integral estimates and to increase unweighting efficiencies.
We propose a method for transforming probability distributions so that parameters of interest are forced into a specified distribution. We prove that this approach is the maximum-entropy choice, and ...provide a motivating example, applicable to neutrino-hierarchy inference.
We determine the upper limit on the mass of the lightest neutrino from the most robust recent cosmological and terrestrial data. Marginalizing over possible effective relativistic degrees of freedom ...at early times (Neff) and assuming normal mass ordering, the mass of the lightest neutrino is less than 0.037 eV at 95% confidence; with inverted ordering, the bound is 0.042 eV. These results improve upon the strength and robustness of other recent limits and constrain the mass of the lightest neutrino to be barely larger than the largest mass splitting. We show the impacts of realistic mass models and different sources of Neff.
The overall cosmological parameter tension between the Atacama Cosmology Telescope 2020 fourth data release (ACT) and Planck 2018 data within the concordance cosmological model is quantified using ...the Suspiciousness statistic to be 2.6 σ . Between ACT and the South Pole Telescope (SPT) we find a tension of 2.4 σ , and 2.8 σ between ACT and Planck + SPT combined. While it is unclear whether the tension is caused by statistical fluctuations, systematic effects or new physics, caution should be exercised in combining these cosmic microwave background datasets in the context of the Λ CDM standard model of the universe.
Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the past decade. ...The full configuration interaction quantum Monte Carlo (FCIQMC) method allows one to systematically approach the exact solution of such problems, for cases where very high accuracy is desired. The introduction of FCIQMC has subsequently led to the development of coupled cluster Monte Carlo (CCMC) and density matrix quantum Monte Carlo (DMQMC), allowing stochastic sampling of the coupled cluster wave function and the exact thermal density matrix, respectively. In this Article, we describe the HANDE-QMC code, an open-source implementation of FCIQMC, CCMC and DMQMC, including initiator and semistochastic adaptations. We describe our code and demonstrate its use on three example systems; a molecule (nitric oxide), a model solid (the uniform electron gas), and a real solid (diamond). An illustrative tutorial is also included.
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