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DOE OSTI2021

A semiparametric latent factor model for large scale temporal data with heteroscedasticity

Large scale temporal data have flourished in a vast array of applications, and their sophisticated structures, especially the heteroscedasticity among subjects with inter- and intra-temporal dependence, have fueled a great demand for new statistical models. In this paper, with covariate information, we consider a flexible model for large scale temporal data with subject-specific heteroscedasticity. Formally, the model employs latent semiparametric factors to simultaneously account for the subject-specific heteroscedasticity and the contemporaneous and/or serial correlations. The subject-specific heteroscedasticity is modeled as the product of the unobserved factor process and subject’s covariate effect, which is further characterized via additive models. For estimation, we propose a two-step procedure. First, the latent factor process and nonparametric loading are recovered through projection-based methods, and following, we estimate the regression components by approaches motivated from the generalized least squares. By scrupulously examining the non-asymptotic rates for recovering the factor process and its loading, we show the consistency and efficiency of estimated regression coefficients in the absence of prior knowledge of latent factor process and subject’s covariate effect. Here, the statistical guarantees remain valid even for finite time points that makes our method particularly appealing when the subjects significantly outnumber the observation time points. Using comprehensive simulations, we demonstrate the finite sample performance of our method, which corroborates the theoretical findings. Finally, we apply our method to a data set of air quality and energy consumption collected at 129 monitoring sites in the United States in 2015.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1986

Evolution of the luminosity function of extragalactic objects

A nonparametric procedure for determining the evolution of the luminosity function (LF) of extragalactic objects is described. The following steps are required: (1) selection of complete samples with known observational selection effects, (2) choice of a cosmological model, (3) statistical analysis of the sample and determination of the evolution of the luminosity function, and (4) the use of the luminosity function for the determination of the formation rate and the physical evolution of the objects. When the present technique is applied to a sample of optically selected quasars with redshifts less than two, it is shown that the LF evolves more strongly for higher luminosities, indicating a larger quasar activity at earlier epochs and a more rapid evolution of the objects during their higher luminosity phases.

Petrosian, V.↗

NASA NTRS2022

NASA Engineering and Safety Center Technical Bulletin No. 22-04: Uncertainty Quantification of Reduced Order Structural Dynamic Models

Uncertainty quantification (UQ) provides statistical bounds on prediction accuracy based on finite element model (FEM) uncertainty. An alternate method for UQ, called the Hybrid Parametric Variation (HPV) combines a parametric variation of the Hurty/Craig-Bampton (HCB) fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method. 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.

Uncertainty Quantification↗

DOE OSTI2021

A Bayesian nonparametric analysis for zero-inflated multivariate count data with application to microbiome study

High-throughput sequencing technology has enabled researchers to profile microbial communities from a variety of environments, but analysis of multivariate taxon count data remains challenging. Here, we develop a Bayesian nonparametric (BNP) regression model with zero inflation to analyse multivariate count data from microbiome studies. A BNP approach flexibly models microbial associations with covariates, such as environmental factors and clinical characteristics. The model produces estimates for probability distributions which relate microbial diversity and differential abundance to covariates, and facilitates community comparisons beyond those provided by simple statistical tests. We compare the model to simpler models and popular alternatives in simulation studies, showing, in addition to these additional community-level insights, it yields superior parameter estimates and model fit in various settings. The model's utility is demonstrated by applying it to a chronic wound microbiome data set and a Human Microbiome Project data set, where it is used to compare microbial communities present in different environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1978

Nonparametric algorithms for the search of signals

Two algorithms for the search of signals in noise are constructed. Two independent measurable properties of a discreet time-dependent stochastic process F are described. The functions A sub K and B sub K fully satisfy conditions for the application of a test based on Spearman's rank correlation coefficient. A statistic to which the one-sided signal test can be applied is constructed under sufficiently natural assumptions about the noise process. The constructed statistics are simplified. Processing results from calculations of statistics constructed for concrete processes are presented.

Myshenkova, T. S.↗

NASA NTRSDate not supplied

Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method

Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.

Uncertainty Quantification↗

NASA NTRS1987

Variability analysis in low count rate sources

A method, based on the chi-square statistics, is described for detecting pulselike time variability in low count rate sources observed with photon-counting instruments. This method can be used even in the presence of observational gaps, takes full advantage of the filtering effect due to binning with different bin sizes, and takes into account the arbitrariness introduced by the binning phase. The procedure developed to limit the dependence of the results on the binning phase and ensure statistically correct results is described along with the application of the proposed procedure to a model of a variable source. Monte Carlo simulations are used to show how the method can be used to derive the characteristic variability time scales and that the method is more sensitive than the nonparametric Kolmogorov-Smirnov test in detecting variability to a given confidence level.

Collura, A.↗

NASA NTRS2019

New Approach for Temporal Stability Evaluation of Pseudo-Invariant Calibration Sites (PICS)

Pseudo-Invariant Calibration Sites (PICS) are one of the most popular methods for in-flight vicarious radiometric calibration of Earth remote sensing satellites. The fundamental question of PICS temporal stability has not been adequately addressed. However, the main purpose of this work is to evaluate the temporal stability of a few PICS using a new approach. The analysis was performed over six PICS (Libya 1, Libya 4, Niger 1, Niger 2, Egypt 1 and Sudan 1). The concept of a “Virtual Constellation” was developed to provide greater temporal coverage and also to overcome the dependence limitation of any specific characteristic derived from one particular sensor. TOA reflectance data from four sensors consistently demonstrating “stable” calibration to within 5%—the Landsat 7 ETM+ (Enhanced Thematic Mapper Plus), Landsat 8 OLI (Operational Land Imager), Terra MODIS (Moderate Resolution Imaging Spectroradiometer) and Sentinel-2A MSI (Multispectral Instrument)–were merged into a seamless dataset. Instead of using the traditional method of trend analysis (Student’s T test), a nonparametric Seasonal Mann-Kendall test was used for determining the PICS stability. The analysis results indicate that Libya 4 and Egypt 1 do not exhibit any monotonic trend in six reflective solar bands common to all of the studied sensors, indicating temporal stability. A decreasing monotonic trend was statistically detected in all bands, except SWIR 2, for Sudan 1 and the Green and Red bands for Niger 1. An increasing trend was detected in the Blue band for Niger 2 and the NIR band for Libya 1. These results do not suggest abandoning PICS as a viable calibration source. Rather, they indicate that PICS temporal stability cannot be assumed and should be regularly monitored as part of the sensor calibration process.

Tuli, Fatima Tuz Zafrin↗

DOE OSTI2023

Deep nonparametric estimation of intrinsic data structures by chart autoencoders: Generalization error and robustness

Autoencoders have demonstrated remarkable success in learning low-dimensional latent features of high-dimensional data across various applications. Assuming that data are sampled near a low-dimensional manifold, we employ chart autoencoders, which encode data into low-dimensional latent features on a collection of charts, preserving the topology and geometry of the data manifold. Our paper establishes statistical guarantees on the generalization error of chart autoencoders, and we demonstrate their denoising capabilities by considering n noisy training samples, along with their noise-free counterparts, on a d-dimensional manifold. By training autoencoders, we show that chart autoencoders can effectively denoise the input data with normal noise. We prove that, under proper network architectures, chart autoencoders achieve a squared generalization error in the order of n–$\frac{2}{d+2}$log 4 n, which depends on the intrinsic dimension of the manifold and only weakly depends on the ambient dimension and noise level. We further extend our theory on data with noise containing both normal and tangential components, where chart autoencoders still exhibit a denoising effect for the normal component. As a special case, our theory also applies to classical autoencoders, as long as the data manifold has a global parametrization. Furthermore, our results provide a solid theoretical foundation for the effectiveness of autoencoders, which is further validated through several numerical experiments.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1986

Statistical methods for astronomical data with upper limits. II - Correlation and regression

Statistical methods for calculating correlations and regressions in bivariate censored data where the dependent variable can have upper or lower limits are presented. Cox's regression and the generalization of Kendall's rank correlation coefficient provide significant levels of correlations, and the EM algorithm, under the assumption of normally distributed errors, and its nonparametric analog using the Kaplan-Meier estimator, give estimates for the slope of a regression line. Monte Carlo simulations demonstrate that survival analysis is reliable in determining correlations between luminosities at different bands. Survival analysis is applied to CO emission in infrared galaxies, X-ray emission in radio galaxies, H-alpha emission in cooling cluster cores, and radio emission in Seyfert galaxies.

Isobe, T.↗

NASA NTRS1987

New methods and results for quantification of lightning-aircraft electrodynamics

The NASA F-106 collected data on the rates of change of electromagnetic parameters on the aircraft surface during over 700 direct lightning strikes while penetrating thunderstorms at altitudes from 15,000 t0 40,000 ft (4,570 to 12,190 m). These in situ measurements provided the basis for the first statistical quantification of the lightning electromagnetic threat to aircraft appropriate for determining indirect lightning effects on aircraft. These data are used to update previous lightning criteria and standards developed over the years from ground-based measurements. The proposed standards will be the first which reflect actual aircraft responses measured at flight altitudes. Nonparametric maximum likelihood estimates of the distribution of the peak electromagnetic rates of change for consideration in the new standards are obtained based on peak recorder data for multiple-strike flights. The linear and nonlinear modeling techniques developed provide means to interpret and understand the direct-strike electromagnetic data acquired on the F-106. The reasonable results obtained with the models, compared with measured responses, provide increased confidence that the models may be credibly applied to other aircraft.

Pitts, Felix L.↗

NASA NTRS1975

A sequential nonparametric pattern classification algorithm based on the Wald SPRT

A sequential nonparametric pattern classification procedure is presented. The method presented is an estimated version of the Wald sequential probability ratio test (SPRT). This method utilizes density function estimates, and the density estimate used is discussed, including a proof of convergence in probability of the estimate to the true density function. The classification procedure proposed makes use of the theory of order statistics, and estimates of the probabilities of misclassification are given. The procedure was tested on discriminating between two classes of Gaussian samples and on discriminating between two kinds of electroencephalogram (EEG) responses.

Poage, J. L.↗

NASA NTRS2005

Adaptive Filtering Using Recurrent Neural Networks

A method for adaptive (or, optionally, nonadaptive) filtering has been developed for estimating the states of complex process systems (e.g., chemical plants, factories, or manufacturing processes at some level of abstraction) from time series of measurements of system inputs and outputs. The method is based partly on the fundamental principles of the Kalman filter and partly on the use of recurrent neural networks. The standard Kalman filter involves an assumption of linearity of the mathematical model used to describe a process system. The extended Kalman filter accommodates a nonlinear process model but still requires linearization about the state estimate. Both the standard and extended Kalman filters involve the often unrealistic assumption that process and measurement noise are zero-mean, Gaussian, and white. In contrast, the present method does not involve any assumptions of linearity of process models or of the nature of process noise; on the contrary, few (if any) assumptions are made about process models, noise models, or the parameters of such models. In this regard, the method can be characterized as one of nonlinear, nonparametric filtering. The method exploits the unique ability of neural networks to approximate nonlinear functions. In a given case, the process model is limited mainly by limitations of the approximation ability of the neural networks chosen for that case. Moreover, despite the lack of assumptions regarding process noise, the method yields minimum- variance filters. In that they do not require statistical models of noise, the neural- network-based state filters of this method are comparable to conventional nonlinear least-squares estimators.

Parlos, Alexander G.↗

DOE OSTI2024

Nonparametric Multiparticle Set Methods for Interpreting Environmental Samples

Collection and analysis of environmental samples is commonly used by a range of stakeholders in nuclear safeguards and security contexts. While the ubiquity of samples and their transport in the environment allow regular collection, developing and demonstrating methods for analyzing these samples is difficult. In this work, an environmental sample consists of a set of one or more individual particles. Recent advances in reactor simulation have allowed us to generate data that are more representative of real-world environmental samples, enabling statistically defensible method development and testing. The most notable of these advances is a drastic increase in the number of material depletion regions, which allows our simulations to capture the variation in isotopic composition seen at length scales consistent with environmental samples. Traditional approaches for handling multiparticle samples treat each particle in the sample individually, estimating the quantity of interest (e.g., core-average burnup) resulting from measurement and analysis of signatures (e.g., nuclide assays) from each individual particle. Individual estimates are then averaged to generate a single estimate of the quantity of interest over the entire sample. In this presentation, we introduce two novel approaches for interpreting environmental samples that comprise of multiple particles: (1) the Quantile-Quantile Comparator, which uses a multivariate generalization of quantile-quantile plots for comparing unknown statistical distributions, and (2) the Set Transformer, an attention-based neural network module designed to model interactions among elements (particles) in the input set (sample). Statistically representative sampling cannot be guaranteed as samples are passively collected and are beholden to what particles are available in the environment. These new analysis methods for set-input problems are expected to be more robust than traditional approaches to issues of sampling bias where particles are not uniformly distributed throughout regions of interest, as well as generally outperform traditional approaches by jointly considering all elements in the set. We will present results comparing the performance of traditional single particle approaches and the novel Quantile-Quantile Comparator and Set Transformer for interpretation of simulated environmental samples.

Phathanapirom, Birdy↗

NASA NTRS2010

Model Robust Calibration: Method and Application to Electronically-Scanned Pressure Transducers

This article presents the application of a recently developed statistical regression method to the controlled instrument calibration problem. The statistical method of Model Robust Regression (MRR), developed by Mays, Birch, and Starnes, is shown to improve instrument calibration by reducing the reliance of the calibration on a predetermined parametric (e.g. polynomial, exponential, logarithmic) model. This is accomplished by allowing fits from the predetermined parametric model to be augmented by a certain portion of a fit to the residuals from the initial regression using a nonparametric (locally parametric) regression technique. The method is demonstrated for the absolute scale calibration of silicon-based pressure transducers.

Walker, Eric L.↗

DOE OSTI2024

Modeling Spatial Asymmetries in Teleconnected Extreme Temperatures

Abstract Combining strengths from deep learning and extreme value theory can help describe complex relationships between variables where extreme events have significant impacts (e.g., environmental or financial applications). Neural networks learn complicated nonlinear relationships from large datasets under limited parametric assumptions. By definition, the number of occurrences of extreme events is small, which limits the ability of the data-hungry, nonparametric neural network to describe rare events. Inspired by recent extreme cold winter weather events in North America caused by atmospheric blocking, we examine several probabilistic generative models for the entire multivariate probability distribution of daily boreal winter surface air temperature. We propose metrics to measure spatial asymmetries, such as long-range anticorrelated patterns that commonly appear in temperature fields during blocking events. Compared to vine copulas, the statistical standard for multivariate copula modeling, deep learning methods show improved ability to reproduce complicated asymmetries in the spatial distribution of ERA5 temperature reanalysis, including the spatial extent of in-sample extreme events.

Krock, Mitchell L.↗

NASA NTRS1980

Numerical trials of HISSE

The mathematical description and implementation of the statistical estimation procedure known as the Houston integrated spatial/spectral estimator (HISSE) is discussed. HISSE is based on a normal mixture model and is designed to take advantage of spectral and spatial information of LANDSAT data pixels, utilizing the initial classification and clustering information provided by the AMOEBA algorithm. The HISSE calculates parametric estimates of class proportions which reduce the error inherent in estimates derived from typical classify and count procedures common to nonparametric clustering algorithms. It also singles out spatial groupings of pixels which are most suitable for labeling classes. These calculations are designed to aid the analyst/interpreter in labeling patches with a crop class label. Finally, HISSE's initial performance on an actual LANDSAT agricultural ground truth data set is reported.

Peters, C.↗

DOE OSTI2022

Probing parity violation with the four-point correlation function of BOSS galaxies

Parity-violating physics in the early universe can leave detectable traces in late-time observables. While vector- and tensor-type parity violation can be observed in the B -modes of the cosmic microwave background, scalar-type signatures are visible only in the four-point correlation function (4PCF) and beyond. This work presents a blind test for parity violation in the 4PCF of the baryon oscillation spectroscopic survey (BOSS) CMASS sample, considering galaxy separations in the range [20; 160]h -1 Mpc The parity-odd 4PCF contains no contributions from standard Λ CDM physics and can be efficiently measured using recently developed estimators. Data are analyzed using both a nonparametric rank test (comparing the BOSS 4PCFs to those of realistic simulations) and a compressed χ 2 analysis, with the former avoiding the assumption of a Gaussian likelihood. These find similar results, with the rank test giving a detection probability of 99.6% (2.9 σ). This provides significant evidence for parity violation, from either cosmological sources or systematics. We perform a number of systematic tests: although these do not reveal any observational artifacts, we cannot exclude the possibility that our detection is caused by the simulations not faithfully representing the statistical properties of the BOSS data. Our measurements can be used to constrain physical models of parity violation. As an example, we consider a coupling between the inflaton and a U (1) gauge field and place bounds on the latter’s energy density, which are several orders of magnitude stronger than those previously reported. Upcoming probes such as DESI and Euclid will reveal whether our detection of parity violation is due to new physics, and strengthen the bounds on a variety of models.

79 ASTRONOMY AND ASTROPHYSICS↗