Theory of time-varying spectral analysis and complex Wishart matrix processes
Distributional results pertaining to complex Wishart processes and time varying spectral estimators on null hypothesis of stationary Gaussian time series
Dubman, M. R.↗
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Results for “wishart”
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Wishart variate generators
Subroutine WSHRT for generating matrix of variances and covariances of Wishart distribution
Smith, W. B.↗
The Effect of the Prior and the Experimental Design on the Inference of the Precision Matrix in Gaussian Chain Graph Models
Here, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model, especially the interplay between the design, the effect of the experiment and prior knowledge about the effect. Estimation of the precision matrix is a fundamental task to infer biological graphical structures like microbial networks. We compare the marginal posterior precision of the precision matrix under four priors: flat, conjugate Normal-Wishart, Normal-MGIG and a general independent. Under the flat and conjugate priors, the Laplace-approximated posterior precision is not a function of the design matrix rendering useless any efforts to find an optimal experimental design to infer the precision matrix. In contrast, the Normal-MGIG and general independent priors do allow for the search of optimal experimental designs, yet there is a sharp upper bound on the information that can be extracted from a given experiment. We confirm our theoretical findings via a simulation study comparing (i) the KL divergence between prior and posterior and (ii) the Stein’s loss difference of MAPs between random and no experiment. Our findings provide practical advice for domain scientists conducting experiments to better infer the precision matrix as a representation of a biological network.
54 ENVIRONMENTAL SCIENCES↗
Bayesian mixture model approach to quantifying the empirical nuclear saturation point
The equation of state (EOS) in the limit of infinite symmetric nuclear matter exhibits an equilibrium density, $n_0 \approx 0.16 \, \mathrm{fm}^{-3}$, at which the pressure vanishes and the energy per particle attains its minimum, $E_0 \approx -16 \, \mathrm{MeV}$. Although not directly measurable, the nuclear saturation point $(n_0,E_0)$ can be extrapolated by density functional theory (DFT), providing tight constraints for microscopic interactions derived from chiral effective field theory (EFT). However, when considering several DFT predictions for $(n_0,E_0)$ from Skyrme and Relativistic Mean Field (RMF) models together, a discrepancy between these model classes emerges at high confidence levels that each model prediction's uncertainty cannot explain. How can we leverage these DFT constraints to rigorously benchmark nuclear saturation properties of chiral interactions? To address this question, we present a Bayesian mixture model that combines multiple DFT predictions for $(n_0,E_0)$ using an efficient conjugate prior approach. The inferred posterior distribution for the saturation point's mean and covariance matrix follows a Normal-inverse-Wishart class, resulting in posterior predictives in the form of correlated, bivariate $t$-distributions. The DFT uncertainty reports are then used to mix these posteriors using an ordinary Monte Carlo approach. At the 95\% credibility level, we estimate $n_0 \approx 0.157 \pm 0.010 \, \mathrm{fm}^{-3}$ and $E_0 \approx -15.97 \pm 0.40 \, \mathrm{MeV}$ for the marginal (univariate) $t$-distributions. Combined with chiral EFT calculations of the pure neutron matter EOS, we obtain bivariate normal distributions for the nuclear symmetry energy and its slope parameter evaluated at $n_0$: $S_v \approx 32.0 \pm 1.1 \, \mathrm{MeV}$ and $L\approx 52.6\pm 8.1 \, \mathrm{MeV}$ (95\%), respectively. Furthermore, our Bayesian framework is publicly available, so practitioners can readily use and extend our results.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Development of an open-source regional data assimilation system in PEcAn v. 1.7.2: application to carbon cycle reanalysis across the contiguous US using SIPNET
Abstract. The ability to monitor, understand, and predict the dynamics of the terrestrial carbon cycle requires the capacity to robustly and coherently synthesize multiple streams of information that each provide partial information about different pools and fluxes. In this study, we introduce a new terrestrial carbon cycle data assimilation system, built on the PEcAn model–data eco-informatics system, and its application for the development of a proof-of-concept carbon “reanalysis” product that harmonizes carbon pools (leaf, wood, soil) and fluxes (GPP, Ra, Rh, NEE) across the contiguous United States from 1986–2019. We first calibrated this system against plant trait and flux tower net ecosystem exchange (NEE) using a novel emulated hierarchical Bayesian approach. Next, we extended the Tobit–Wishart ensemble filter (TWEnF) state data assimilation (SDA) framework, a generalization of the common ensemble Kalman filter which accounts for censored data and provides a fully Bayesian estimate of model process error, to a regional-scale system with a calibrated localization. Combined with additional workflows for propagating parameter, initial condition, and driver uncertainty, this represents the most complete and robust uncertainty accounting available for terrestrial carbon models. Our initial reanalysis was run on an irregular grid of ∼ 500 points selected using a stratified sampling method to efficiently capture environmental heterogeneity. Remotely sensed observations of aboveground biomass (Landsat LandTrendr) and leaf area index (LAI) (MODIS MOD15) were sequentially assimilated into the SIPNET model. Reanalysis soil carbon, which was indirectly constrained based on modeled covariances, showed general agreement with SoilGrids, an independent soil carbon data product. Reanalysis NEE, which was constrained based on posterior ensemble weights, also showed good agreement with eddy flux tower NEE and reduced root mean square error (RMSE) compared to the calibrated forecast. Ultimately, PEcAn's new open-source regional data assimilation framework provides a scalable workflow for harmonizing multiple data constraints and providing a uniform synthetic platform for carbon monitoring, reporting, and verification (MRV) as well as accelerating terrestrial carbon cycle research.
54 ENVIRONMENTAL SCIENCES↗
Characterizations of linear sufficient statistics
A surjective bounded linear operator T from a Banach space X to a Banach space Y must be a sufficient statistic for a dominated family of probability measures defined on the Borel sets of X. These results were applied, so that they characterize linear sufficient statistics for families of the exponential type, including as special cases the Wishart and multivariate normal distributions. The latter result was used to establish precisely which procedures for sampling from a normal population had the property that the sample mean was a sufficient statistic.
Peters, B. C., Jr.↗
Computational Bayesian Methods Applied to Complex Problems in Bio and Astro Statistics
In this dissertation we apply computational Bayesian methods to three distinct problems. In the first chapter, we address the issue of unrealistic covariance matrices used to estimate collision probabilities. We model covariance matrices with a Bayesian Normal-Inverse-Wishart model, which we fit with Gibbs sampling. In the second chapter, we are interested in determining the sample sizes necessary to achieve a particular interval width and establish non-inferiority in the analysis of prevalences using two fallible tests. To this end, we use a third order asymptotic approximation. In the third chapter, we wish to synthesize evidence across multiple domains in measurements taken longitudinally across time, featuring a substantial amount of structurally missing data, and fit the model with Hamiltonian Monte Carlo in a simulation to analyze how estimates of a parameter of interest change across sample sizes.
Elrod, Chris↗
Uncertainty Models for the Hybrid Parametric Variation Method of Uncertainty Quantification; Analysis
There is some level of uncertainty in every finite element model (FEM), which flows to a level of uncertainty in predicted results. The purpose of uncertainty quantification (UQ) is to provide statistical bounds on prediction accuracy based on model uncertainty. This is distinct from model updating, which attempts to modify models to improve their accuracy. UQ does not improve the accuracy of models, but accepts that the models are inherently inaccurate and attempts to quantify the impact of that inaccuracy on predicted results. Previously, an alternate method for UQ, called the Hybrid Parametric Variation (HPV) method, was applied to Space Launch System (SLS) Hurty/Craig-Bampton (HCB) components to predict system-level statistics for launch vehicle attitude control transfer functions and core stage section loads due to buffet. The HPV method combines a parametric variation of the HCB fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method that randomly varies the HCB mass and stiffness matrices as Wishart random matrix distributions using random matrix theory (RMT). Alternatively, the most common method for modeling uncertainty in the structural dynamics community is a parametric approach, which varies physical parameters in the model. However, there are several disadvantages associated with the parametric method. Determining a reduced set of parameters that have a significant impact on the system response can be time consuming, and the selected parameter probability distributions are rarely reliably known. Therefore, in practice, the parameters are surrogates for the actual errors, and the link to parameter uncertainty is unknown. Another major drawback is that the uncertainty that can be represented is limited to the form of the nominal FEM. It is the experience of the authors that based on numerous aerospace programs, almost all FEM errors are in form rather than parameter values. This hypothesis is supported by the observation of the authors that it is almost never possible to ‘tune’ a FEM to match modal test results by only modifying model parameters. Model-form uncertainty cannot be directly represented by FEM input parameters nor included in a parametric approach. However, model-form uncertainty can be modeled using RMT, where a probability distribution is developed for the matrix ensemble of interest. The major advantage of the NPV method is that it covers errors in model form. The HPV method anchors uncertainty at the HCB component level to component modal test results by matching the HCB and test modes based on mode descriptions or other methods, and then applying differing levels of frequency variation. The specific variations depend on the confidence to which a component FEM has been validated through modal testing. The NPV method is layered on the frequency variation to match modal test self-orthogonality and cross-orthogonality (XO) results. Once the component uncertainty models are identified, they are assembled, and the uncertainty is propagated to the system level using a Monte Carlo (MC) analysis approach that generates statistics for system-level predictions This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The second example is an application to a component that is design specific to the SLS. Based on this work and other assessments, the HPV method provides another tool to the toolset used for complex system UQ analysis. From experience gathered to date using the HPV method, additional design specific applications must be investigated to provide further confidence in the validity of the HPV method of UQ analysis.
Uncertainty quantification↗
What’s Next in Regional (Air) Mobility? Finding the next possible big ideas in selected problems
This presentation summarizes studies ongoing under the "What's Next in Regional (Air) Mobility" umbrella within the Intercenter Systems Analysis Team. It includes a look at the Regional Air Mobility (RAM) market potential, simulation of a RAM passenger network to gather statistics, and scrutinizes airport energy needs to support RAM operations. It also references a companion presentation provided by the DOT Volpe Center presented by Jacob Wishart related to RAM market and demand estimates.
Advanced Air Mobility↗
Investigating corrosion behavior of Ni and Ni-20Cr in molten ZnCl2
Explore the source record for details and available documents.
99 GENERAL AND MISCELLANEOUS↗
Connections between the Speciation and Solubility of Ni(II) and Co(II) in Molten ZnCl2
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99 GENERAL AND MISCELLANEOUS↗
Radiation-Assisted Formation of Metal Nanoparticles in Molten Salts
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99 GENERAL AND MISCELLANEOUS↗
Interfacial Speciation Determines Interfacial Chemistry: X-ray-Induced Lithium Fluoride Formation from Water-in-salt Electrolytes on Solid Surfaces
Using synchrotron X-rays the LiTFSI/H 2 O electrolyte interfacial decomposition pathways in the „water-in-salt“ and „salt-in-water“ regimes are investigated. The resultant photoelectron-induced reduction was revealed to be concentration-dependent interfacial chemistry that only occurs among closely contact ion-pairs, which constitutes the rationale behind the „water-in-salt“ concept.
38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
Interfacial Speciation Determines Interfacial Chemistry: X‐ray‐Induced Lithium Fluoride Formation from Water‐in‐salt Electrolytes on Solid Surfaces
Not Available
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
X‐Ray Absorption Studies of Local Structure of Dilute Ionic Species in Molten Salts
Molten salts are crucial materials with exceptional properties that make them suitable for applications such as heat transfer media, coolants, and liquid fuels in molten salt nuclear reactors and the concentrated solar power industry. Understanding their properties requires unraveling the intricate mysteries of their structure. To achieve this, advanced characterization tools are essential. Among various techniques, X‐ray absorption fine structure (XAFS) stands out as a versatile method capable of studying the structure of molten salts under in situ conditions. This review highlights recent advancements in the application of XAFS for investigating the local structure of molten salts, discusses its limitations and potential improvements, and explores complementary approaches such as simulations, machine learning, and correlative experimental methods.
22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
Visualizing time-dependent microstructural and chemical evolution during molten salt corrosion of Ni-20Cr model alloy using correlative quasi in situ TEM and in situ synchrotron X-ray nano-tomography
In situ monitoring of corrosion processes is important to fundamentally understand the kinetics and evolution of materials in harsh environments. A quasi in situ transmission electron microscopy technique was utilized to study microstructural and chemical evolution of a Ni-20Cr disc sample 6 exposed to molten KCl-MgCl 2 salt for 60 s in consecutive 20 s iterations. In situ synchrotron X-ray nano-tomography was performed to characterize the morphological evolution of a Ni-20Cr microwire exposed to molten KCl-MgCl 2 . Here, both techniques captured key corrosion events and revealed mechanisms at different time and length scales, potentially bringing greater insights and 10 deeper understanding beyond conventional analysis.
36 MATERIALS SCIENCE↗
Electrochemical noise studies on localized corrosion of Ni and Ni-20Cr in molten ZnCl 2
The electrochemical noise (ECN) technique was employed to study corrosion of two model systems, i.e. pure Ni and a binary Ni-20 wt%Cr (Ni20Cr) alloy in molten ZnCl 2 at 623 K. Here we measured ECN transients in current and open-circuit potential from two nominally identical Ni-Ni and Ni20Cr-Ni20Cr electrodes and one galvanic Ni-Ni20Cr electrode pair. The behavior of ECN is quite distinct among the three-electrode systems, and it is correlated with the various microscopic observations of micro- and nano-scale morphological features. Based on the ECN study coupled with the microstructural analysis, the origins of ECN in the molten salt environment as well as the mechanisms of localized corrosion in the three systems are discussed.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
How alkyl branching shapes structure in imidazolium and pyrrolidinium NTf 2 ionic liquids
High-energy X-ray scattering experiments and molecular dynamics (MD) simulations were carried out on ionic liquids (ILs) consisting of 1-alkyl-3-methylimidazolium and 1-alkyl-1-methylpyrrolidinium cations. These cations were paired with bis(trifluoromethylsulfonyl)amide anions and identical alkyl tails were used for both cationic species. The goal of this work is to investigate how the nanoscale structure of the ionic liquid changes with the length and with the degree of branching of the alkyl tail, for ILs having a common anion. We investigate spatial correlations in the intermolecular region, focusing on the intrinsic charge-charge interactions that characterize all ionic liquids, as well as the nanoscale domain segregation that is present in IL species with significant nonpolar components.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗