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DOE OSTI2022

An Exact and Near-Exact Distribution Approach to the Behrens–Fisher Problem

The Behrens–Fisher problem occurs when testing the equality of means of two normal distributions without the assumption that the two variances are equal. This paper presents approaches based on the exact and near-exact distributions for the test statistic of the Behrens–Fisher problem, depending on different combinations of even or odd sample sizes. We present the exact distribution when both sample sizes are odd and the near-exact distribution when one or both sample sizes are even. The near-exact distributions are based on a finite mixture of generalized integer gamma (GIG) distributions, used as an approximation to the exact distribution, which consists of an infinite series. The proposed tests, based on the exact and the near-exact distributions, are compared with Welch’s t-test through Monte Carlo simulations, in particular for small and unbalanced sample sizes. The results show that the proposed approaches are competent solutions to the Behrens–Fisher problem, exhibiting precise sizes and better powers than Welch’s approach for those cases. Numerical studies show that the Welch’s t-test tends to be a bit more conservative than the test statistics based on the exact or near-exact distribution, in particular when sample sizes are small and unbalanced, situations in which the proposed exact or near-exact distributions obtain higher powers than Welch’s t-test.

Hong, Serim↗

NASA NTRS2007

SEM-EDS Analyses of Small Craters in Stardust Aluminum Foils: Implications for the Wild-2 Dust Distribution

Aluminium foils were used on Stardust to stabilize the aerogel specimens in the modular collector tray. Part of these foils were fully exposed to the flux of cometary grains emanating from Wild 2. Because the exposed part of these foils had to be harvested before extraction of the aerogel, numerous foil strips some 1.7 mm wide and 13 or 33 mm long were generated during Stardusts's Preliminary Examination (PE). These strips are readily accommodated in their entirety in the sample chambers of modern SEMs, thus providing the opportunity to characterize in situ the size distribution and residue composition - employing EDS methods - of statistically more significant numbers of cometary dust particles compared to aerogel, the latter mandating extensive sample preparation. We describe here the analysis of nearly 300 impact craters and their implications for Wild 2 dust.

Borg, J.↗

DOE OSTI2017

Final Report: Quantification of Uncertainty in Extreme Scale Computations (QUEST)

QUEST (\url{www.quest-scidac.org}) is a SciDAC Institute that is focused on uncertainty quantification (UQ) in large-scale scientific computations. Our goals are to (1) advance the state of the art in UQ mathematics, algorithms, and software; and (2) provide modeling, algorithmic, and general UQ expertise, together with software tools, to other SciDAC projects, thereby enabling and guiding a broad range of UQ activities in their respective contexts. QUEST is a collaboration among six institutions (Sandia National Laboratories, Los Alamos National Laboratory, the University of Southern California, Massachusetts Institute of Technology, the University of Texas at Austin, and Duke University) with a history of joint UQ research. Our vision encompasses all aspects of UQ in leadership-class computing. This includes the well-founded setup of UQ problems; characterization of the input space given available data/information; local and global sensitivity analysis; adaptive dimensionality and order reduction; forward and inverse propagation of uncertainty; handling of application code failures, missing data, and hardware/software fault tolerance; and model inadequacy, comparison, validation, selection, and averaging. The nature of the UQ problem requires the seamless combination of data, models, and information across this landscape in a manner that provides a self-consistent quantification of requisite uncertainties in predictions from computational models. Accordingly, our UQ methods and tools span an interdisciplinary space across applied math, information theory, and statistics. The MIT QUEST effort centers on statistical inference and methods for surrogate or reduced-order modeling. MIT personnel have been responsible for the development of adaptive sampling methods, methods for approximating computationally intensive models, and software for both forward uncertainty propagation and statistical inverse problems. A key software product of the MIT QUEST effort is the MIT Uncertainty Quantification library, called MUQ (\url{muq.mit.edu}).

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1989

Do the major axes of rich clusters of galaxies point toward their neighbors?

The major axis orientation of rich clusters of galaxies, determined from an analysis of X-ray images, is used to investigate whether these clusters point toward their nearest neighbors. No statistical significance is found for a pointing effect between clusters and their nearest neighbors in either X-ray, optical, or combined X-ray and optical samples. Using updated redshifts and permitting nonstatistical sample Abell clusters as nearest neighbors does not affect this conclusion. The lack of statistical significance for a pointing effect favors hierarchical models in which galaxies form first, followed by clusters and then superclusters. For clusters with well-defined X-ray orientations, it is found that cluster position angles determined from X-ray and optical data are in general agreement.

Ulmer, M. P.↗

DOE OSTI2020

Methodology for the development of empirical models relating 13C NMR spectral features to fuel properties

Effective formulation of new gasoline or diesel fuels for internal combustion engines would benefit from the development of reliable models for predicting key fuel properties based on a set of molecular descriptors obtained from a single measurement. This is particularly relevant in the case of renewable fuels, where the available fuel sample quantity may be limited. In this work, we present a statistically-based methodology for building empirical models to predict multiple properties from one-dimensional 13C nuclear magnetic resonance (NMR) spectra measured on around 200 microliters of a liquid fuel. NMR spectra contain information about the molecular composition of a sample and the carbon types and molecular substructures therein. Our approach uses this information to build sparse, interpretable models, where the predicted properties are linked to specific molecular features. The approach takes into consideration the constrained nature of the features making up the one-dimensional NMR spectrum, which, after standardization, represent a relative fuel composition. We point to the limitations in interpretability that arise when building this type of empirical predictive model and suggest how these limitations may be diminished. Among the many properties important for maximizing engine performance and minimizing emissions, we build models that predict derived cetane number and distillation temperatures as these are of particular interest because of their links to fuel economy, drivability, and engine-out emissions. Results suggest that the properties of interest may be impacted by only a few of the 27 13C NMR regions represented in the data, pointing to new directions for further testing in the development of improved fuels.

predictive models, biofuels., NMR Analysis↗

NASA NTRS1976

Multivariate normality

Sets of experimentally determined or routinely observed data provide information about the past, present and, hopefully, future sets of similarly produced data. An infinite set of statistical models exists which may be used to describe the data sets. The normal distribution is one model. If it serves at all, it serves well. If a data set, or a transformation of the set, representative of a larger population can be described by the normal distribution, then valid statistical inferences can be drawn. There are several tests which may be applied to a data set to determine whether the univariate normal model adequately describes the set. The chi-square test based on Pearson's work in the late nineteenth and early twentieth centuries is often used. Like all tests, it has some weaknesses which are discussed in elementary texts. Extension of the chi-square test to the multivariate normal model is provided. Tables and graphs permit easier application of the test in the higher dimensions. Several examples, using recorded data, illustrate the procedures. Tests of maximum absolute differences, mean sum of squares of residuals, runs and changes of sign are included in these tests. Dimensions one through five with selected sample sizes 11 to 101 are used to illustrate the statistical tests developed.

Crutcher, H. L.↗

DOE OSTI2025

Intrinsic Kinetics of Polyethylene Terephthalate Pyrolysis via Micropyrolysis and Multivariate Chromatographic Analysis

This study provides an in-depth investigation of the primary decomposition of polyethylene terephthalate (PET) via pyrolysis, employing an experimental-analytic workflow that integrates design of experiments (DoE), micropyrolysis coupled with comprehensive two-dimensional gas chromatography (GC×GC), and multivariate data analysis to verify intrinsic kinetic conditions and elucidate evolving product distributions for mapping key reaction pathways. Peaks that could not be identified using commercial spectral libraries were assigned using Mass Frontier simulations, enabling the identification of divinyl terephthalate, ethyl vinyl terephthalate, and 2-(benzoyloxy)ethyl vinyl terephthalate. A polar×polar (non-orthogonal) column set tailored for the detection of carboxylic acids enhanced the quantification of benzoic acid, 4-vinylbenzoic acid, 4-ethylbenzoic acid, and methylbenzoic acid by up to 6-fold relative to an orthogonal column combination (non-polar×mid-polar). Moreover, pyrolysis variables were systematically evaluated using a Box- Behnken design (BBD), encompassing pyrolysis temperature (500−600 °C), sample weight (50−150 μg), and carrier gas flow rate (100−300 mL min −1 ). Among these, pyrolysis temperature was the only statistically significant factor influencing product yields, ranging from 58.78 to 84.26 wt %. In contrast, neither the sample weight nor the carrier gas flow rate had a significant effect on product yields within the evaluated experimental space. At 600 °C, the major pyrolysis products were benzoic acid (up to 20.20 ± 1.46 wt %) and CO 2 (up to 21.28 ± 1.46 wt %), which can be produced through decarboxylation reactions. These findings underscore the critical importance of selecting appropriate analytical columns for the accurate quantification of heteroatomcontaining products such as carboxylic acids, which may otherwise be underestimated or undetected due to their reactivity with the stationary phase of non-polar and mid-polar columns, as well as other GC components. They also highlight the importance of selecting pyrolysis conditions for investigating the primary decomposition of PET under an isothermal kinetically limited regime.

aromatic compounds↗

DOE OSTI2023

Critical assessment of the recent report on the gigaparsec-scale correlation of the orientations of large quasar groups

ABSTRACT Recently, it was reported that large quasar groups (LQGs) identified from the Sloan Digital Sky Survey (SDSS) data release seven catalogue are not randomly oriented but preferentially aligned or orthogonal over scales 1–2 Gpc. To confirm this claim, I reproduced the same LQG sample and performed Sobolev tests of uniformity on the LQG orientation axes in the redshift space. Contrary to the original report based on the bimodal distribution of the LQG position angles in the sky, I found no departure from uniformity in the distribution of the LQG orientation axes. I also examined whether the LQGs are physical structures using a statistically more reliable data set constructed from the SDSS data release 16 (DR16) large-scale structure (LSS) quasar catalogue. Considering the Gaussian primordial density fluctuations and shot noise, I estimated the mass density contrasts of the LQGs from the number counts of the DR16 LSS quasars and found that most of the LQGs do not trace statistically significant high-density regions. I conclude that the LQG sample is a collection of unphysical chance associations and should not be used for any cosmological studies.

Fujii, Hirokazu (ORCID:0000000161473512)↗

DOE OSTI2026

Structured illumination for surface-resolved grazing-incidence X-ray scattering

Grazing-incidence (GI) scattering techniques are widely used to characterize thin films, offering high surface sensitivity and insight into morphology and structure. However, these approaches typically provide statistical averaged information due to elongated footprint or limited spatial resolution due to beam size. Here we introduce a method that combines structured illumination with GI X-ray scattering and leverages our computational imaging approach to resolve local structural details. We demonstrate that our method captures local features of an organic semiconductor thin film without the need for sample rotation as in tomography. The method expands GI techniques from statistical averaging to high-resolution imaging, thereby providing the capability for detailed analysis of local material properties, such as domain shape, orientation and polymorphism, which are critical for advancing material design towards more efficient and tailored materials.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1977

A model for simulating random atmospheres as a function of latitude, season, and time

An empirical stochastic computer model was developed with the capability of generating random thermodynamic profiles of the atmosphere below an altitude of 99 km which are characteristic of any given season, latitude, and time of day. Samples of temperature, density, and pressure profiles generated by the model are statistically similar to measured profiles in a data base of over 6000 rocket and high-altitude atmospheric soundings; that is, means and standard deviations of modeled profiles and their vertical gradients are in close agreement with data. Model-generated samples can be used for Monte Carlo simulations of aircraft or spacecraft trajectories to predict or account for the effects on a vehicle's performance of atmospheric variability. Other potential uses for the model are in simulating pollutant dispersion patterns, variations in sound propagation, and other phenomena which are dependent on atmospheric properties, and in developing data-reduction software for satellite monitoring systems.

Campbell, J. W.↗

DOE OSTI2015

Identification of discriminant proteins through antibody profiling, methods and apparatus for identifying an individual

A method for determining a plurality of proteins for discriminating and positively identifying an individual based from a biological sample. The method may include profiling a biological sample from a plurality of individuals against a protein array including a plurality of proteins. The protein array may include proteins attached to a support in a preselected pattern such that locations of the proteins are known. The biological sample may be contacted with the protein array such that a portion of antibodies in the biological sample reacts with and binds to the proteins forming immune complexes. A statistical analysis method, such as discriminant analysis, may be performed to determine discriminating proteins for distinguishing individuals. Proteins of interest may be used to form a protein array. Such a protein array may be used, for example, to compare a forensic sample from an unknown source with a sample from a known source.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2016

Identification of discriminant proteins through antibody profiling, methods and apparatus for identifying an individual

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

A critical assessment of solutions to the galaxy diversity problem

Galactic rotation curves exhibit a diverse range of inner slopes. Observational data indicates that explaining this diversity may require a mechanism that correlates a galaxy's surface brightness with the central-most region of its dark matter halo. Here, in this work, we compare several concrete models that capture the relevant physics required to explain the galaxy diversity problem. We focus specifically on a Self-Interacting Dark Matter (SIDM) model with an isothermal core and two Cold Dark Matter (CDM) models with/without baryonic feedback. In contrast to the CDM case, the SIDM model can lead to the formation of an isothermal core in the halo, and is also mostly insensitive to baryonic feedback processes, which act on longer time-scales. Using rotation curves from 90 galaxies in the Spitzer Photometry & Accurate Rotation Curves (SPARC) catalog, we perform a comprehensive model comparison that addresses issues of statistical methodology from prior works. The best-fit halo models that we recover are consistent with standard CDM concentration-mass and abundance matching relations. We find that both the SIDM and feedback-affected CDM models are better than a CDM model with no feedback in explaining the rotation curves of low and high surface brightness galaxies in the sample. However, when compared to each other, there is no strong statistical preference for either the SIDM or the feedback-affected CDM halo model as the source of galaxy diversity in the SPARC catalog.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

SU-E-T-769: T-Test Based Prior Error Estimate and Stopping Criterion for Monte Carlo Dose Calculation in Proton Therapy

Purpose: The Monte Carlo (MC) method is a gold standard for dose calculation in radiotherapy. However, it is not a priori clear how many particles need to be simulated to achieve a given dose accuracy. Prior error estimate and stopping criterion are not well established for MC. This work aims to fill this gap. Methods: Due to the statistical nature of MC, our approach is based on one-sample t-test. We design the prior error estimate method based on the t-test, and then use this t-test based error estimate for developing a simulation stopping criterion. The three major components are as follows.First, the source particles are randomized in energy, space and angle, so that the dose deposition from a particle to the voxel is independent and identically distributed (i.i.d.).Second, a sample under consideration in the t-test is the mean value of dose deposition to the voxel by sufficiently large number of source particles. Then according to central limit theorem, the sample as the mean value of i.i.d. variables is normally distributed with the expectation equal to the true deposited dose.Third, the t-test is performed with the null hypothesis that the difference between sample expectation (the same as true deposited dose) and on-the-fly calculated mean sample dose from MC is larger than a given error threshold, in addition to which users have the freedom to specify confidence probability and region of interest in the t-test based stopping criterion. Results: The method is validated for proton dose calculation. The difference between the MC Result based on the t-test prior error estimate and the statistical Result by repeating numerous MC simulations is within 1%. Conclusion: The t-test based prior error estimate and stopping criterion are developed for MC and validated for proton dose calculation. Xiang Hong and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500)

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

Classification of Malaysia aromatic rice using multivariate statistical analysis

Aromatic rice (Oryza sativa L.) is considered as the best quality premium rice. The varieties are preferred by consumers because of its preference criteria such as shape, colour, distinctive aroma and flavour. The price of aromatic rice is higher than ordinary rice due to its special needed growth condition for instance specific climate and soil. Presently, the aromatic rice quality is identified by using its key elements and isotopic variables. The rice can also be classified via Gas Chromatography Mass Spectrometry (GC-MS) or human sensory panels. However, the uses of human sensory panels have significant drawbacks such as lengthy training time, and prone to fatigue as the number of sample increased and inconsistent. The GC–MS analysis techniques on the other hand, require detailed procedures, lengthy analysis and quite costly. This paper presents the application of in-house developed Electronic Nose (e-nose) to classify new aromatic rice varieties. The e-nose is used to classify the variety of aromatic rice based on the samples odour. The samples were taken from the variety of rice. The instrument utilizes multivariate statistical data analysis, including Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA) and K-Nearest Neighbours (KNN) to classify the unknown rice samples. The Leave-One-Out (LOO) validation approach is applied to evaluate the ability of KNN to perform recognition and classification of the unspecified samples. The visual observation of the PCA and LDA plots of the rice proves that the instrument was able to separate the samples into different clusters accordingly. The results of LDA and KNN with low misclassification error support the above findings and we may conclude that the e-nose is successfully applied to the classification of the aromatic rice varieties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Comparison between mirror Langmuir probe and gas-puff imaging measurements of intermittent fluctuations in the Alcator C-Mod scrape-off layer

Statistical properties of the scrape-off layer plasma fluctuations are studied in ohmically heated plasmas in the Alcator C-Mod tokamak. For the first time, plasma fluctuations as well as parameters that describe the fluctuations are compared across measurements from a mirror Langmuir probe (MLP) and from gas-puff imaging (GPI) that sample the same plasma discharge. This comparison is complemented by an analysis of line emission time-series data, synthesized from the MLP electron density and temperature measurements. The fluctuations observed by the MLP and GPI typically display relative fluctuation amplitudes of order unity together with positively skewed and flattened probability density functions. Such data time series are well described by an established stochastic framework that models the data as a superposition of uncorrelated, two-sided exponential pulses. The most important parameter of the process is the intermittency parameter, $γ=τ_d/τ_w$, where τd denotes the duration time of a single pulse and $τ_w$ gives the average waiting time between consecutive pulses. In this study we show, using a new deconvolution method, that these parameters can be consistently estimated from different statistics of the data. We also show that the statistical properties of the data sampled by the MLP and GPI diagnostic are very similar. Finally, a synthetic GPI signal using only plasma parameters sampled by the MLP shows qualitatively different fluctuation statistics from the measured GPI signal.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Multifidelity uncertainty quantification with models based on dissimilar parameters

Multifidelity uncertainty quantification (MF UQ) sampling approaches have been shown to significantly reduce the variance of statistical estimators while preserving the bias of the highest-fidelity model, provided that the low-fidelity models are well correlated. However, maintaining a high level of correlation can be challenging, especially when models depend on different input uncertain parameters, which drastically reduces the correlation. Existing MF UQ approaches do not adequately address this issue. In this work, we propose a new sampling strategy that exploits a shared space to improve the correlation among models with dissimilar parameterization. We achieve this by transforming the original coordinates onto an auxiliary manifold using the adaptive basis (AB) method (Tipireddy and Ghanem, 2014). The AB method has two main benefits: (1) it provides an effective tool to identify the low-dimensional manifold on which each model can be represented, and (2) it enables easy transformation of polynomial chaos representations from high- to low-dimensional spaces. This latter feature is used to identify a shared manifold among models without requiring additional evaluations. Here we present two algorithmic flavors of the new estimator to cover different analysis scenarios, including those with legacy and non-legacy high-fidelity (HF) data. We provide numerical results for analytical examples, a direct field acoustic test, and a finite element model of a nuclear fuel assembly. For all examples, we compare the proposed strategy against both single-fidelity and MF estimators based on the original model parameterization.

42 ENGINEERING↗

DOE OSTI2020

Characterization and differentiation of aluminum powders used in improvised explosive devices – Part 1: Proof of concept of the utility of particle micromorphometry

Abstract Aluminum (Al) powders are commonly used in improvised explosive devices as metallic fuels, a component of explosive mixtures. These powders can be obtained readily from industrial‐scale and consumer products, and produced using unsophisticated “kitchen chemistry” techniques. This research demonstrates the potential of automated particle micromorphometry for comparisons between known source and questioned Al powders recovered from IEDs, as well as for insight into the method of Al powder manufacture. Al powder samples were obtained from legitimate manufacturers, and 56 samples were produced “in‐house” from Al‐containing spray paints and ball‐milled Al foils. Transmitted light microscope images of Al powder particles were acquired using an automated stage with automated z‐focus; 17 size and shape parameters were measured for all particles. Approximately 37,000–2,500,000 particles/sample were analyzed using an open‐source statistical package with customized code. Dimensionality reduction was required for processing the large datasets: eight of the 17 measured variables were selected based on inspection of the correlation matrix. Data from four subsamples from each of the 56 samples produced using “in‐house” methods were analyzed using ANOVA to assess the within‐ and between‐sample variation. High within‐sample variation was noted; however, ANOVA and post‐hoc Tukey's honestly significant difference (HSD) tests demonstrated that the between‐sample variation was substantially larger than the within‐sample variation. Each sample could be differentiated from all other samples in the test set. Future experiments will focus on ways to reduce the within‐sample variation, and additional statistical and microanalytical methods to classify sources and confidently constrain the method of Al powder manufacture.

Baldaino, JenaMarie↗