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Sample variance in the local measurements of the Hubble constant
The current >3σ tension between the Hubble constant H 0 measured from local distance indicators and from cosmic microwave background is one of the most highly debated issues in cosmology, as it possibly indicates new physics or unknown systematics. In this work, we explore whether this tension can be alleviated by the sample variance in the local measurements, which use a small fraction of the Hubble volume. We use a large-volume cosmological N-body simulation to model the local measurements and to quantify the variance due to local density fluctuations and sample selection. We explicitly take into account the inhomogeneous spatial distribution of type Ia supernovae. Despite the faithful modelling of the observations, our results confirm previous findings that sample variance in the local Hubble constant ($H$ $^{loc}_{0}$) measurements is small; we find σ ($H$ $^{loc}_{0}$)=0.31km s -1 Mpc -1 a nearly negligible fraction of the ~6 km s -1 Mpc -1 necessary to explain the difference between the local and global H 0 measurements. While the H 0 tension could in principle be explained by our local neighbourhood being a underdense region of radius ~150 Mpc, the extreme required underdensity of such a void (δ ≃ -0.8) makes it very unlikely in a ΛCDM universe, and it also violates existing observational constraints. Furthermore, sample variance in a ΛCDM universe cannot appreciably alleviate the tension in H 0 measurements even after taking into account the inhomogeneous selection of type Ia supernovae.
Applications of non-parametric statistics and analysis of variance on sample variances
Nonparametric methods that are available for NASA-type applications are discussed. An attempt will be made here to survey what can be used, to attempt recommendations as to when each would be applicable, and to compare the methods, when possible, with the usual normal-theory procedures that are avavilable for the Gaussion analog. It is important here to point out the hypotheses that are being tested, the assumptions that are being made, and limitations of the nonparametric procedures. The appropriateness of doing analysis of variance on sample variances are also discussed and studied. This procedure is followed in several NASA simulation projects. On the surface this would appear to be reasonably sound procedure. However, difficulties involved center around the normality problem and the basic homogeneous variance assumption that is mase in usual analysis of variance problems. These difficulties discussed and guidelines given for using the methods.
Modality-Driven Classification and Visualization of Ensemble Variance
Paper for the IEEE Visualization Conference Advances in computational power now enable domain scientists to address conceptual and parametric uncertainty by running simulations multiple times in order to sufficiently sample the uncertain input space.
A Simple Algorithm for Approximating Confidence on the Modified Allan Variance and the Time Variance
An approximating algorithm for computing equvalent degrees of freedom of the Modified Allan Variance and its square root, the Modified Allan Deviation (MVAR and MDEV), and the Time Variance and Time Deviation (TVAR and TDEV) is presented, along with an algorithm for approximating the inverse chi-square distribution.
INTERPRETING MAGNETIC VARIANCE ANISOTROPY MEASUREMENTS IN THE SOLAR WIND
The magnetic variance anisotropy (A{sub m}) of the solar wind has been used widely as a method to identify the nature of solar wind turbulent fluctuations; however, a thorough discussion of the meaning and interpretation of the A{sub m} has not appeared in the literature. This paper explores the implications and limitations of using the A{sub m} as a method for constraining the solar wind fluctuation mode composition and presents a more informative method for interpreting spacecraft data. The paper also compares predictions of the A{sub m} from linear theory to nonlinear turbulence simulations and solar wind measurements. In both cases, linear theory compares well and suggests that the solar wind for the interval studied is dominantly Alfvenic in the inertial and dissipation ranges to scales of k{rho}{sub i} {approx_equal} 5.
Application of regression, variance, and density based global sensitivity methods to integrated VERA-CS and BISON simulations [Application of regression, variance, and density based global sensitivity methods to integrated VERA-CS and BISON simulations]
Uncertainty quantification (UQ) and sensitivity analyses (SA) are performed for coupled simulations between VERA-CS, a coupled pin resolved neutron transport and subchannel thermal hydraulics code, and the fuel performance code BISON. The interface between VERA-CS and BISON is performed in a multiphysics environment known as the LOCA Toolkit for U.S. light water reactors (LOTUS) currently under development at Idaho National Laboratory (INL). A focus is placed on using a variety of SA measures, including two regression based (Pearson and Spearman), one variance based (Sobol indices), and three moment independent measures (Delta moment independent measures with L 1 , L 2 , and L ∞ norms). The problem under inspection is a single assembly depletion case for three fuel cycles. The figures of merit are the minimum departure from nucleate boiling ratio (MDNBR), maximum fuel centerline temperature (MFCT), and gap conductance at peak power (GCPP). SA results show MDNBR to be linear with consistent rankings throughout the fuel cycles. MFCT is linear, but with a change in rankings at the switch from open gap to closed gap models. GCPP is nonlinear at intermediate states that coincide with the onset of contact between fuel and cladding. Furthermore, these nonlinear states allow for the showcasing of higher order SA measures over first order methods.
Variance-Reduced Splitting Schemes for Monotone Stochastic Generalized Equations
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Confidence regions for variance ratios in variance components models
Statistical mechanics for constructing confidence intervals for variance ratios in balanced and unbalanced experimental designs
Self-Consistent Field Methods for Excited States in Strong Magnetic Fields: A Comparison Between Energy - and Variance-based Approaches
An efficient implementation of geometrical derivatives at the Hartree–Fock (HF) and current-density functional theory (CDFT) levels is presented for the study of molecular structure in strong magnetic fields. The required integral derivatives are constructed using a hybrid McMurchie–Davidson and Rys quadrature approach, which combines the amenability of the former to the evaluation of derivative integrals with the efficiency of the latter for basis sets with high angular momentum. In addition to its application to evaluating derivatives of four-center integrals, this approach is also applied to gradients using the resolution-of-the-identity approximation, enabling efficient optimization of molecular structure for many-electron systems under a strong magnetic field. The CDFT contributions have been implemented for a wide range of density functionals up to and including the meta-GGA level with current-density dependent contributions and (range-separated) hybrids for the first time. Illustrative applications are presented to the OH and benzene molecules, revealing the rich and complex chemistry induced by the presence of an external magnetic field. Challenges for geometry optimization in strong fields are highlighted, along with the requirement for careful analysis of the resulting electronic structure at each stationary point. The importance of correlation effects is examined by comparison of results at the HF and CDFT levels. The present implementation of molecular gradients at the CDFT level provides a cost-effective approach to the study of molecular structure under strong magnetic fields, opening up many new possibilities for the study of chemistry in this regime.
Understanding the (co)variance in petrophysical properties of CO 2 reservoirs comprising sedimentary architecture
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Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty
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Relationship between sensitivity indices defined by variance- and covariance-based methods
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More than Drought: Precipitation Variance, Excessive Wetness, Pathogens and the Future of the Western Edge of the Eastern Deciduous Forest
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