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NASA NTRS2000

Paralinear Oxidation of CVD SiC in Simulated Fuel-Rich Combustion

The oxidation kinetics of CVD SiC were measured by thermogravimetric analysis (TGA) in a 4H2 (central dot) 12H2O (central dot) 10CO (central dot) 7CO2 (central dot) 67N2 gas mixture flowing at 0.44 cm/s at temperatures between 1300 and 1450 C in fused quartz furnace tubes at I atm total pressure. The SiC was oxidized to form solid SiO2. At less than or = 1350 C, the SiO2 was in turn volatilized. Volatilization kinetics were consistent with the thermodynamic predictions based on SiO formation. These two simultaneous reactions resulted in overall paralinear kinetics. A curve fitting technique was used to determine the linear and parabolic rate constants from the paralinear kinetic data. Volatilization of the protective SiO2 scale resulted in accelerated consumption of SiC. Recession rates under conditions more representative of actual combustors were estimated from the furnace data.

Fox, Dennis S.↗
NASA NTRS2002

Small-Scale Tropopause Dynamics and TOMS Total Ozone

This project used Earth Probe Total Ozone Mapping Spectrometer (EP TOMS) along-track ozone retrievals, in conjunction with ancillary meteorological fields and modeling studies, for high resolution investigations of upper troposphere and lower stratosphere dynamics. Specifically, high resolution along-track (Level 2) EP TOMS data were used to investigate the beautiful fine-scale structure in constituent and meteorological fields prominent in the evolution of highly non-linear baroclinic storm systems. Comparison was made with high resolution meteorological models. The analyses provide internal consistency checks and validation of the EP TOMS data which are vital for monitoring ozone depletion in both polar and midlatitude regions.

Stanford, John L.↗
NASA NTRS2003

Grid-Independent Large-Eddy Simulation in Turbulent Channel Flow using Three-Dimensional Explicit Filtering

In this paper, turbulence-closure models are evaluated using the 'true' LES approach in turbulent channel flow. The study is an extension of the work presented by Gullbrand (2001), where fourth-order commutative filter functions are applied in three dimensions in a fourth-order finite-difference code. The true LES solution is the grid-independent solution to the filtered governing equations. The solution is obtained by keeping the filter width constant while the computational grid is refined. As the grid is refined, the solution converges towards the true LES solution. The true LES solution will depend on the filter width used, but will be independent of the grid resolution. In traditional LES, because the filter is implicit and directly connected to the grid spacing, the solution converges towards a direct numerical simulation (DNS) as the grid is refined, and not towards the solution of the filtered Navier-Stokes equations. The effect of turbulence-closure models is therefore difficult to determine in traditional LES because, as the grid is refined, more turbulence length scales are resolved and less influence from the models is expected. In contrast, in the true LES formulation, the explicit filter eliminates all scales that are smaller than the filter cutoff, regardless of the grid resolution. This ensures that the resolved length-scales do not vary as the grid resolution is changed. In true LES, the cell size must be smaller than or equal to the cutoff length scale of the filter function. The turbulence-closure models investigated are the dynamic Smagorinsky model (DSM), the dynamic mixed model (DMM), and the dynamic reconstruction model (DRM). These turbulence models were previously studied using two-dimensional explicit filtering in turbulent channel flow by Gullbrand & Chow (2002). The DSM by Germano et al. (1991) is used as the USFS model in all the simulations. This enables evaluation of different reconstruction models for the RSFS stresses. The DMM consists of the scale-similarity model (SSM) by Bardina et al. (1983), which is an RSFS model, in linear combination with the DSM. In the DRM, the RSFS stresses are modeled by using an estimate of the unfiltered velocity in the unclosed term, while the USFS stresses are modeled by the DSM. The DSM and the DMM are two commonly used turbulence-closure models, while the DRM is a more recent model.

Gullbrand, Jessica↗
NASA NTRS2003

VPS GRCop-84 Liner Development Efforts

For the past several years, NASA's Marshall Space Flight Center (MSFC) has been working with Plasma Processes, Inc. (PPI) to fabricate combustion chamber liners using the Vacuum Plasma Spray (VPS) process. Multiple liners of a variety of shapes and sizes have been created. Each liner has been fabricated with GRCop-84 (a copper alloy with chromium and niobium) and a functional gradient coating (FGC) on the hot wall. While the VPS process offers versatility and a reduced fabrication schedule, the material system created with VPS allows the liners to operate at higher temperatures, with maximum blanch resistance and improved cycle life. A subscal unit (5K lbf thrust class) is being cycle tested in a LOX/Hydrogen thrust chamber assembly at MSFC. To date, over 75 hot-fire tests have been accumulated on this article. Tests include conditions normally detrimental to conventional materials, yet the VPS GRCop-84 liner has yet to show any signs of degradation. A larger chamber (15K lbf thrust class) has also been fabricated and is being prepared for hot-fire testing at MSFC near the end of 2003. Linear liners have been successfully created to further demonstrate the versatility of the process. Finally, scale up issues for the VPS process are being tackled with efforts to fabricate a full size, engine class liner. Specifically, a liner for the SSME's Main Combustion Chamber (MCC) has recently been attempted. The SSME size was chosen for convenience, since its design was readily available and its size was sufficient to tackle specific issues. Efforts to fabricate these large liners have already provided valuable lessons for using this process for engine programs. The material quality for these large units is being evaluated with destructive analysis and these results will be available by the end of 2003.

Elam, Sandra K.↗
NASA NTRS2005

Data Images and Other Graphical Displays for Directional Data

Vectors, axes, and periodic phenomena have direction. Directional variation can be expressed as points on a unit circle and is the subject of circular statistics, a relatively new application of statistics. An overview of existing methods for the display of directional data is given. The data image for linear variables is reviewed, then extended to directional variables by displaying direction using a color scale composed of a sequence of four or more color gradients with continuity between sequences and ordered intuitively in a color wheel such that the color of the 0deg angle is the same as the color of the 360deg angle. Cross over, which arose in automating the summarization of historical wind data, and color discontinuity resulting from the use a single color gradient in computational fluid dynamics visualization are eliminated. The new method provides for simultaneous resolution of detail on a small scale and overall structure on a large scale. Example circular data images are given of a global view of average wind direction of El Nino periods, computed rocket motor internal combustion flow, a global view of direction of the horizontal component of earth's main magnetic field on 9/15/2004, and Space Shuttle solid rocket motor nozzle vectoring.

Morphet, Bill↗
NASA NTRS2009

Three-dimensional Finite Element Formulation and Scalable Domain Decomposition for High Fidelity Rotor Dynamic Analysis

This paper has two objectives. The first objective is to formulate a 3-dimensional Finite Element Model for the dynamic analysis of helicopter rotor blades. The second objective is to implement and analyze a dual-primal iterative substructuring based Krylov solver, that is parallel and scalable, for the solution of the 3-D FEM analysis. The numerical and parallel scalability of the solver is studied using two prototype problems - one for ideal hover (symmetric) and one for a transient forward flight (non-symmetric) - both carried out on up to 48 processors. In both hover and forward flight conditions, a perfect linear speed-up is observed, for a given problem size, up to the point of substructure optimality. Substructure optimality and the linear parallel speed-up range are both shown to depend on the problem size as well as on the selection of the coarse problem. With a larger problem size, linear speed-up is restored up to the new substructure optimality. The solver also scales with problem size - even though this conclusion is premature given the small prototype grids considered in this study.

Datta, Anubhav↗
NASA NTRS2011

Correlations in the (Sub)Mil1imeter Background from ACT x BLAST

We present measurements of the auto- and cross-frequency correlation power spectra of the cosmic (sub)millimeter background at: 250, 350, and 500 microns (1200, 860, and 600 GHz) from observations made with the Balloon-borne Large Aperture Submillimeter Telescope, BLAST; and at 1380 and 2030 microns (218 and 148 GHz) from observations made with the Atacama Cosmology Telescope, ACT. The overlapping observations cover 8.6 deg(sup 2) in an area relatively free of Galactic dust near the south ecliptic pole (SEP). The ACT bands are sensitive to radiation from the CMB, the Sunyaev-Zel'dovich (SZ) effect from galaxy clusters, and to emission by radio and dusty star-forming galaxies (DSFGs), while the dominant contribution to the BLAST bands is from DSFGs. We confirm and extend the BLAST analysis of clustering with an independent pipeline, and also detect correlations between the ACT and BLAST maps at over 25(sigma) significance, which we interpret as a detection of the DSFGs in the ACT maps. In addition to a Poisson component in the cross-frequency power spectra, we detect a clustered signal at 4(sigma), and using a model for the DSFG evolution and number counts, we successfully fit all our spectra with a linear clustering model and a bias that depends only on red shift and not on scale. Finally, the data are compared to, and generally agree with, phenomenological models for the DSFG population. This study represents a first of its kind, and demonstrates the constraining power of the cross-frequency correlation technique to constrain models for the DSFGs. Similar analyses with more data will impose tight constraints 011 future models.

Hajian, Amir↗
NASA NTRSDate not supplied

Sleep, Sleepiness, and Performance Across Three In-Flight Bunk Rest Opportunities

Introduction: Airline pilots are required to take a rest break in a bunk during long-haul flights in an effort to reduce sleepiness during critical phases of flight. It is unclear, however, whether each rest break affords equal opportunity for sleep. We aimed to characterize sleep, sleepiness, and performance outcomes across three in-flight rest breaks during long-haul flights. Methods: Thirty-seven pilots wore actiwatches and completed sleep diaries for approximately two weeks while flying a variety of long-haul routes (n=126 flights). Self-reported in-flight bunk rest (BR) periods were used to set rest intervals and sleep was estimated within these intervals using actigraphy software (wake threshold set to medium). Pilots provided Karolinska Sleepiness Scale ratings (KSS) and performed a 5-minute psychomotor vigilance task (PVT) before landing. A linear mixed-effects model with participant included as a random effect and allowed to vary by intercept was used to assess differences between BR opportunities. Results : The majority (97%, n=122) of bunk rest periods contained sleep (as estimated by actigraphy). The mean (+/- standard deviation) sleep duration for the first, middle, and third BR opportunity was 152.8 (69.7), 149.2 (44.1), 125.2 (44.9) minutes, respectively. There was a significant effect of BR opportunity for sleep duration (F2,54 = 3.747, p=.03) and KSS (F2,44 = 7.869, p=.001). Bonferroni adjusted planned pairwise contrasts revealed that pilots using the third BR obtained significantly less sleep than in the first BR (p=.029). KSS ratings prior to landing were higher for the third BR compared to both the first (p=.001) and middle BR (p=.017). There were no significant differences for PVT speed or lapses (all p>05). Conclusion: These results suggest that the last rest break is associated with shorter sleep, lower alertness, and no differences in performance relative to the other rest breaks. Further analysis is required to determine whether the higher KSS ratings following the third rest break are associated with sleep inertia, or whether other factors may be involved.

sleepiness↗
NASA NTRS2023

Characterization of Errors in Satellite-Based HCHO/NO 2 Tropospheric Column Ratios With Respect to Chemistry, Column-to-PBL Translation, Spatial Representation, and Retrieval Uncertainties

The availability of formaldehyde (HCHO) (a proxy for volatile organic compound reactivity) and nitrogen dioxide (NO 2 ) (a proxy for nitrogen oxides) tropospheric columns from ultraviolet–visible (UV–Vis) satellites has motivated many to use their ratios to gain some insights into the near-surface ozone sensitivity. Strong emphasis has been placed on the challenges that come with transforming what is being observed in the tropospheric column to what is actually in the planetary boundary layer (PBL) and near the surface; however, little attention has been paid to other sources of error such as chemistry, spatial representation, and retrieval uncertainties. Here we leverage a wide spectrum of tools and data to quantify those errors carefully. Concerning the chemistry error, a well-characterized box model constrained by more than 500 h of aircraft data from NASA's air quality campaigns is used to simulate the ratio of the chemical loss of HO 2 + RO 2 (LRO x ) to the chemical loss of NO x (LNO x ). Subsequently, we challenge the predictive power of HCHO/NO 2 ratios (FNRs), which are commonly applied in current research, in detecting the underlying ozone regimes by comparing them to LRO x /LNO x . FNRs show a strongly linear (R 2 =0.94) relationship with LRO x /LNO x , but only on the logarithmic scale. Following the baseline (i.e., ln(LRO x /LNO x ) = −1.0 ± 0.2) with the model and mechanism (CB06, r2) used for segregating NO x -sensitive from VOC-sensitive regimes, we observe a broad range of FNR thresholds ranging from 1 to 4. The transitioning ratios strictly follow a Gaussian distribution with a mean and standard deviation of 1.8 and 0.4, respectively. This implies that the FNR has an inherent 20 % standard error (1σ) resulting from not accurately describing the RO x –HO x cycle. We calculate high ozone production rates (PO 3 ) dominated by large HCHO × NO 2 concentration levels, a new proxy for the abundance of ozone precursors. The relationship between PO 3 and HCHO × NO 2 becomes more pronounced when moving towards NO x -sensitive regions due to nonlinear chemistry; our results indicate that there is fruitful information in the HCHO × NO 2 metric that has not been utilized in ozone studies. The vast amount of vertical information on HCHO and NO 2 concentrations from the air quality campaigns enables us to parameterize the vertical shapes of FNRs using a second-order rational function permitting an analytical solution for an altitude adjustment factor to partition the tropospheric columns into the PBL region. We propose a mathematical solution to the spatial representation error based on modeling isotropic semivariograms. Based on summertime-averaged data, the Ozone Monitoring Instrument (OMI) loses 12 % of its spatial information at its native resolution with respect to a high-resolution sensor like the TROPOspheric Monitoring Instrument (TROPOMI) (> 5.5 × 3.5 km 2 ). A pixel with a grid size of 216 km 2 fails at capturing ∼ 65 % of the spatial information in FNRs at a 50 km length scale comparable to the size of a large urban center (e.g., Los Angeles). We ultimately leverage a large suite of in situ and ground-based remote sensing measurements to draw the error distributions of daily TROPOMI and OMI tropospheric NO 2 and HCHO columns. At a 68 % confidence interval (1σ), errors pertaining to daily TROPOMI observations, either HCHO or tropospheric NO 2 columns, should be above 1.2–1.5 × 10 16 molec. cm −2 to attain a 20 %–30 % standard error in the ratio. This level of error is almost non-achievable with the OMI given its large error in HCHO. The satellite column retrieval error is the largest contributor to the total error (40 %–90 %) in the FNRs. Due to a stronger signal in cities, the total relative error (< 50 %) tends to be mild, whereas areas with low vegetation and anthropogenic sources (e.g., the Rocky Mountains) are markedly uncertain (> 100 %). Our study suggests that continuing development in the retrieval algorithm and sensor design and calibration is essential to be able to advance the application of FNRs beyond a qualitative metric.

Amir H. Souri↗
NASA NTRS2015

Projection-Based Reduced Order Modeling for Spacecraft Thermal Analysis

This paper presents a mathematically rigorous, subspace projection-based reduced order modeling (ROM) methodology and an integrated framework to automatically generate reduced order models for spacecraft thermal analysis. Two key steps in the reduced order modeling procedure are described: (1) the acquisition of a full-scale spacecraft model in the ordinary differential equation (ODE) and differential algebraic equation (DAE) form to resolve its dynamic thermal behavior; and (2) the ROM to markedly reduce the dimension of the full-scale model. Specifically, proper orthogonal decomposition (POD) in conjunction with discrete empirical interpolation method (DEIM) and trajectory piece-wise linear (TPWL) methods are developed to address the strong nonlinear thermal effects due to coupled conductive and radiative heat transfer in the spacecraft environment. Case studies using NASA-relevant satellite models are undertaken to verify the capability and to assess the computational performance of the ROM technique in terms of speed-up and error relative to the full-scale model. ROM exhibits excellent agreement in spatiotemporal thermal profiles (<0.5% relative error in pertinent time scales) along with salient computational acceleration (up to two orders of magnitude speed-up) over the full-scale analysis. These findings establish the feasibility of ROM to perform rational and computationally affordable thermal analysis, develop reliable thermal control strategies for spacecraft, and greatly reduce the development cycle times and costs.

0000↗
DOE OSTI2025

Variational quantum and neural quantum states algorithms for the linear complementarity problem

Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ) hardware. Although VQAs have been demonstrated as proofs of concept, their practical utility in solving real-world problems—and whether quantum-inspired classical algorithms can match their performance—remains an open question. We present a novel application of the variational quantum linear solver (VQLS) and its classical neural quantum states-based counterpart, the variational neural linear solver (VNLS), as key components within a minimum map Newton solver for a complementarity-based rigid-body contact model. We demonstrate using the VNLS that our solver accurately simulates the dynamics of rigid spherical bodies during collision events. These results suggest that quantum and quantum-inspired linear algebra algorithms can serve as viable alternatives to standard linear algebra solvers for modelling certain physical systems.

neural quantum states↗
DOE OSTI2022

Scaling of the strange-metal scattering in unconventional superconductors

Marked evolution of properties with minute changes in the doping level is a hallmark of the complex chemistry that governs copper oxide superconductivity as manifested in the celebrated superconducting domes and quantum criticality taking place at precise compositions. The strange-metal state, in which the resistivity varies linearly with temperature, has emerged as a central feature in the normal state of copper oxide superconductors. The ubiquity of this behaviour signals an intimate link between the scattering mechanism and superconductivity. However, a clear quantitative picture of the correlation has been lacking. In this study we report the observation of precise quantitative scaling laws among the superconducting transition temperature (T c ), the linear-in-T scattering coefficient (A 1 ) and the doping level (x) in electron-doped copper oxide La 2-x Ce x CuO 4 (LCCO). High-resolution characterization of epitaxial composition-spread films, which encompass the entire overdoped range of LCCO, has enabled us to systematically map its structural and transport properties with unprecedented accuracy and with increments of Δx = 0.0015. Additionally, we have uncovered the relations T c ~ (x c - x) 0.5 ~ (A 1 $\square$ ) 0.5 , where x c is the critical doping in which superconductivity disappears and A 1 $\square$ is the coefficient of the linear resistivity per CuO 2 plane. The striking similarity of the T c versus A 1 $\square$ relation among copper oxides, iron-based and organic superconductors may be an indication of a common mechanism of the strange-metal behaviour and unconventional superconductivity in these systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Development of a Filtered CFD-DEM Drag Model with Multiscale Markers Using an Artificial Neural Network and Nonlinear Regression

Here, the accuracy of coarse-grained Euler-Lagrangian simulations of fluidized beds heavily depends on the mesoscale drag models to account for the influences of the unresolved sub-grid structures. Traditional filtered drag models are regressed with mesoscale markers such as voidage and slip velocities. In this research, a filtered drag was regressed with both mesoscale and macro-scale markers using fine grid Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) simulations. The traditional non-linear regression method was compared with machine learning regression using an Artificial Neural Network (ANN) implemented in PyTorch and coupled with MFiX. The new drag showed higher accuracy than the Wen-Yu drag and another filtered drag derived from the two-fluid model. The nonlinear regression shows slightly better results than ANN regression in cases with similar R 2 values. The utilization of the gas inlet velocity as an additional macro-scale marker reduced the errors by up to 55.3% in the tested cases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1993

On the response of the tropical atmosphere to large-scale deforestation

Recent studies on the Amazon deforestation problem predict that removal of the forest will result in a higher surface temperature, a significant reduction in evaporation and precipitation, and possibly significant changes in the tropical circulation. Here, we discuss the basic mechanisms contributing to the response of the tropical atmosphere to deforestation. A simple linear model of the tropical atmosphere is used in studying the effects of deforestation on climate. It is suggested that the impact of large-scale deforestation on the circulation of the tropical atmosphere consists of two components: the response of the tropical circulation to the negative change in precipitation (heating), and the response of the same circulation to the positive change in surface temperature. Owing to their different signs, the changes in predicted temperature and precipitation excite competing responses working in opposite directions. The predicted change in tropical circulation determines the change, if any, in atmospheric moisture convergence, which is equivalent to the change in run-off. The dependence of run-off predictions on the relative magnitudes of the predicted changes in precipitation and surface temperature implies that the predictions about run-off are highly sensitive, which explains, at least partly, the disagreement between the different models concerning the sign of the predicted change in Amazonian run-off.

Eltahir, E. A. B.↗
DOE OSTI2023

Holistic fleet optimization incorporating system design considerations

The methodology described in this article enables a type of holistic fleet optimization that simultaneously considers the composition and activity of a fleet through time as well as the design of individual systems within the fleet. Often, real-world system design optimization and fleet-level acquisition optimization are treated separately due to the prohibitive scale and complexity of each problem. Importantly, this means that fleet-level schedules are typically limited to the inclusion of predefined system configurations and are blind to a rich spectrum of system design alternatives. Similarly, system design optimization often considers a system in isolation from the fleet and is blind to numerous, complex portfolio-level considerations. In reality, these two problems are highly interconnected. To properly address this system-fleet design interdependence, we present a general method for efficiently incorporating multi-objective system design trade-off information into a mixed-integer linear programming (MILP) fleet-level optimization. This work is motivated by the authors' experience with large-scale DOD acquisition portfolios. However, the methodology is general to any application where the fleet-level problem is a MILP and there exists at least one system having a design trade space in which two or more design objectives are parameters in the fleet-level MILP.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2018

Overview of Solar-Induced Chlorophyll Fluorescence (SIF) from the Orbiting Carbon Observatory-2: Retrieval, Cross-Mission Comparison, and Global Monitoring for GPP

The Orbiting Carbon Observatory-2 (OCO-2), launched in July 2014, is capable of measuring Solar-Induced chlorophyll Fluorescence (SIF), a functional proxy for terrestrial gross primary productivity (GPP). Although its primary mission is to measure the column-averaged mixing ratio of CO2 (Xco(sub 2)) to constrain global carbon source/sink distribution, one of the OCO-2 spectrometers allows for a robust SIF retrieval solely based on solar Fraunhofer lines. Here we present a technical overview of the OCO-2 SIF product, aiming to provide the scientific community guidance on best practices for data analysis, interpretation, and application. This overview consists of the retrieval algorithms, OCO-2 specific bias correction, retrieval uncertainty evaluation, cross-mission comparison with other existing SIF products, and a global-scale examination of the SIF-GPP relationship. With the initial three years of data (September 2014 onward), we compared OCO-2 SIF with retrievals from Greenhouse Gases Observing Satellite (GOSAT) and Global Ozone Monitoring Experiment-2 (GOME-2), and examined its relationship with FLUXCOM and MODIS GPP datasets. Our results show that OCO-2 SIF, along with GOSAT products, closely resemble the mean spatial and temporal patterns of FLUXCOM GPP from regions to the globe. Compared with GOME-2, however, OCO-2 depicts a more realistic spatial contrast between the tropics and extra-tropics. The linear relationship between OCO-2 SIF and existing modeled GPP products diverges somewhat across biomes at the global scale, consistent with previous GOSAT or GOME-2 based findings when modeled GPP products were used, but in contrast to a consistent cross-biome SIF-GPP relationship obtained at flux tower sites with OCO-2 products. This contrast suggests a critical need to reconcile differences in diverse SIF and GPP products and the relationships among them. Overall, the OCO-2 SIF products are robust and valuable for monitoring the global terrestrial carbon cycle and for constraining the carbon source/sink strengths of the Earth system. Finally, insights are offered for future satellite missions optimized for SIF retrievals.

GPP↗
NASA NTRS1984

Theoretical Modeling for Numerical Weather Prediction

The goal is to utilize predictability theory and numerical experimentation to identify and understand some of the dynamical processes which must be modeled more realistically if large-scale numerical weather predictions are to be improved. The emphasis is on the use of relatively simple models to exlore the properties of physically comprehensive general circulation models (GCM's). A global linear quasi-geostrophic model and the Goddard Laboratory for Atmospheric Sciences (GLAS) GCM were used to investigate several mechanisms which are responsible for the decay of large-scale forecast skill in mid-latitude numerical weather predictions. Five-day forecasts for an ensemble of cases were made using First GARP Global Experiment data. It was found that forecast skill depends crucially on the specification of the stationary forcing. A lack of stationary forcing leads to spurious westwad propagation of the ultralong waves. Forecasts made with stationary forcings derived from climatological data are superior to those using forcings inferred from observations immediately preceding the forecast period. Interhemispheric forecast differences were analyzed, and the model errors were compared to errors of a simple persistence-damped-to-climatology scheme and to errors of the GLAS GCM.

Somerville, R. C. J.↗
DOE OSTI2023

Large-Scale Inference of Multivariate Regression for Heavy-Tailed and Asymmetric Data

Large-scale multivariate regression is a fundamental statistical tool with a wide range of applications. Here, this study considers the problem of simultaneously testing a large number of general linear hypotheses, encompassing covariate-effect analysis, analysis of variance, and model comparisons. The challenge that accompanies a large number of tests is the ubiquitous presence of heavy-tailed and/or highly skewed measurement noise, which is the main reason for the failure of conventional least squares-based methods. For large-scale multivariate regression, we develop a set of robust inference methods to explore data features such as heavy tailedness and skewness, which are not visible to least squares methods. The new testing procedure is based on the data-adaptive Huber regression and a new covariance estimator of regression estimates. Under mild conditions, we show that our methods produce consistent estimates of the false discovery proportion. Extensive numerical experiments and an empirical study on quantitative linguistics demonstrate the advantage of the proposed method over many state-of-the-art methods when the data are generated from heavy-tailed and/or skewed distributions.

97 MATHEMATICS AND COMPUTING↗