Nearest neighbor - A new non-parametric test used for classifying spectral data
Nonparametric statistical interference program for spectral data classification
Chapman, W. E.↗
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Normative Ranges for, and Interrater Reliability of, Rotational Vestibular and Balance Tests in U.S. Military Service Members and Veterans
Purpose: The objectives of this study were to (a) describe normative ranges—expressed as reference intervals (RIs)—for vestibular and balance function tests in a cohort of Service Members and Veterans (SMVs) and (b) to describe the interrater reliability of these tests. Method: As part of the Defense and Veterans Brain Injury Center (DVBIC)/Traumatic Brain Injury Center of Excellence 15-year Longitudinal Traumatic Brain Injury (TBI) Study, participants completed the following: vestibulo-ocular reflex suppression, visual-vestibular enhancement, subjective visual vertical, subjective visual horizontal, sinusoidal harmonic acceleration, the computerized rotational head impulse test (crHIT), and the sensory organization test. RIs were calculated using nonparametric methods and interrater reliability was assessed using intraclass correlation coefficients between three audiologists who independently reviewed and cleaned the data. Results: Reference populations for each outcome measure comprised 40 to 72 individuals, 19 to 61 years of age, who served either as noninjured controls (NIC) or injured controls (IC) in the 15-year study; none had a history of TBI or blast exposure. A subset of 15 SMVs from the NIC, IC, and TBI groups were included in the interrater reliability calculations. RIs are reported for 27 outcome measures from the seven rotational vestibular and balance tests. Interrater reliability was considered excellent for all tests except the crHIT, which was found to have good interrater reliability. Conclusion: This study provides clinicians and scientists with important information regarding normative ranges and interrater reliability for rotational vestibular and balance tests in SMVs.
Audiology & Speech-Language Pathology↗
Compositional studies of primitive asteroids
The composition of primitive asteroids and their relationship to satellites in the solar system will be studied by analyzing existing narrowband charge coupled device (CCD) reflectance spectra, acquiring additional spectra of asteroids and small satellites in the 0.5 to 1.0 micrometer spectral range, and exploring possibilities for obtaining compositional information in the blue-UV spectral region. Comparison with laboratory spectra of terrestrial chlorites and serpentines (phyllosilicates) and the clay minerals found in carbonaceous chondrite meteorites will continue. During 1987, narrowband CCD reflectance spectra of 17 additional asteroids were acquired. These spectra and spectra of 34 other asteroids have been used primarily for two studies: weak absorption features similar to those due to Fe2(+) and Fe2(+) - Fe3(+) transitions in iron oxides f ound in terrestrial chlorites and serpentines and carbonaceous chondrites have been identified in some primitive asteroid spectra. There is a first indication that asteroids grouped by heliocentric distance show similar weak absorption features. Nonparametric statistics are being applied to test the hypothesis of discrete remnants of a gradation in composition of outer-belt asteroids.
Vilas, F.↗
The Statistical Consulting Center for Astronomy (SCCA)
The process by which raw astronomical data acquisition is transformed into scientifically meaningful results and interpretation typically involves many statistical steps. Traditional astronomy limits itself to a narrow range of old and familiar statistical methods: means and standard deviations; least-squares methods like chi(sup 2) minimization; and simple nonparametric procedures such as the Kolmogorov-Smirnov tests. These tools are often inadequate for the complex problems and datasets under investigations, and recent years have witnessed an increased usage of maximum-likelihood, survival analysis, multivariate analysis, wavelet and advanced time-series methods. The Statistical Consulting Center for Astronomy (SCCA) assisted astronomers with the use of sophisticated tools, and to match these tools with specific problems. The SCCA operated with two professors of statistics and a professor of astronomy working together. Questions were received by e-mail, and were discussed in detail with the questioner. Summaries of those questions and answers leading to new approaches were posted on the Web (www.state.psu.edu/ mga/SCCA). In addition to serving individual astronomers, the SCCA established a Web site for general use that provides hypertext links to selected on-line public-domain statistical software and services. The StatCodes site (www.astro.psu.edu/statcodes) provides over 200 links in the areas of: Bayesian statistics; censored and truncated data; correlation and regression, density estimation and smoothing, general statistics packages and information; image analysis; interactive Web tools; multivariate analysis; multivariate clustering and classification; nonparametric analysis; software written by astronomers; spatial statistics; statistical distributions; time series analysis; and visualization tools. StatCodes has received a remarkable high and constant hit rate of 250 hits/week (over 10,000/year) since its inception in mid-1997. It is of interest to scientists both within and outside of astronomy. The most popular sections are multivariate techniques, image analysis, and time series analysis. Hundreds of copies of the ASURV, SLOPES and CENS-TAU codes developed by SCCA scientists were also downloaded from the StatCodes site. In addition to formal SCCA duties, SCCA scientists continued a variety of related activities in astrostatistics, including refereeing of statistically oriented papers submitted to the Astrophysical Journal, talks in meetings including Feigelson's talk to science journalists entitled "The reemergence of astrostatistics" at the American Association for the Advancement of Science meeting, and published papers of astrostatistical content.
Akritas, Michael↗
Applications of non-parametric statistics and analysis of variance on sample variances
Nonparametric methods that are available for NASA-type applications are discussed. An attempt will be made here to survey what can be used, to attempt recommendations as to when each would be applicable, and to compare the methods, when possible, with the usual normal-theory procedures that are avavilable for the Gaussion analog. It is important here to point out the hypotheses that are being tested, the assumptions that are being made, and limitations of the nonparametric procedures. The appropriateness of doing analysis of variance on sample variances are also discussed and studied. This procedure is followed in several NASA simulation projects. On the surface this would appear to be reasonably sound procedure. However, difficulties involved center around the normality problem and the basic homogeneous variance assumption that is mase in usual analysis of variance problems. These difficulties discussed and guidelines given for using the methods.
Myers, R. H.↗
A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior
Most multinomial choice models (e.g., the multinomial logit model) adopted in practice assume an extreme-value Gumbel distribution for the random components (error terms) of utility functions. This distributional assumption offers a closed-form likelihood expression when the utility maximization principle is applied to model choice behaviors. As a result, model coefficients can be easily estimated using the standard maximum likelihood estimation method. However, maximum likelihood estimators are consistent and efficient only if distributional assumptions on the random error terms are valid. It is therefore critical to test the validity of underlying distributional assumptions on the error terms that form the basis of parameter estimation and policy evaluation. In this paper, a practical yet statistically rigorous method is proposed to test the validity of the distributional assumption on the random components of utility functions in both the multinomial logit (MNL) model and multiple discrete-continuous extreme value (MDCEV) model. Based on a semi-nonparametric approach, a closed-form likelihood function that nests the MNL or MDCEV model being tested is derived. The proposed method allows traditional likelihood ratio tests to be used to test violations of the standard Gumbel distribution assumption. Simulation experiments are conducted to demonstrate that the proposed test yields acceptable Type-I and Type-II error probabilities at commonly available sample sizes. The test is then applied to three real-world discrete and discrete-continuous choice models. For all three models, the proposed test rejects the validity of the standard Gumbel distribution in most utility functions, calling for the development of robust choice models that overcome adverse effects of violations of distributional assumptions on the error terms in random utility functions.
30 DIRECT ENERGY CONVERSION↗
Some analysis on the diurnal variation of rainfall over the Atlantic Ocean
Data collected from the GARP Atlantic Tropical Experiment (GATE) was examined. The data were collected from 10,000 grid points arranged as a 100 x 100 array; each grid covered a 4 square km area. The amount of rainfall was measured every 15 minutes during the experiment periods using c-band radars. Two types of analyses were performed on the data: analysis of diurnal variation was done on each of grid points based on the rainfall averages at noon and at midnight, and time series analysis on selected grid points based on the hourly averages of rainfall. Since there are no known distribution model which best describes the rainfall amount, nonparametric methods were used to examine the diurnal variation. Kolmogorov-Smirnov test was used to test if the rainfalls at noon and at midnight have the same statistical distribution. Wilcoxon signed-rank test was used to test if the noon rainfall is heavier than, equal to, or lighter than the midnight rainfall. These tests were done on each of the 10,000 grid points at which the data are available.
Gill, T.↗
The X-ray luminosity function of very rich clusters and the luminosity-richness relation
For a sample of galactic clusters that includes richness class three, four, and five clusters, the significance of the luminosity-richness relation is estimated using nonparametric methods which are valid for any luminosity function. The Kolmogorov-Smirnov test is used to determine the significance at which the X-ray luminosities of clusters in one richness class are statistically equal to those in another. The a priori expectation that the high richness clusters are more luminous on average than lower richness objects is confirmed, but it is found that the luminosity function for clusters of richness class three or higher turns over for luminosities less than about 3 x 10 to the 44th ergs/s, while that for lower richness classes extends to at least an order of magnitude lower luminosity.
Soltan, A.↗
System identification requirements for high-bandwidth rotorcraft flight control system design
The application of system identification methods to high-bandwidth rotorcraft flight control system design is examined. Flight test and modeling requirements are illustrated using flight test data from a BO-105 hingeless rotor helicopter. The proposed approach involves the identification of nonparametric frequency-response models followed by parametric (transfer funtion and state space) model identification. Results for the BO-105 show the need for including coupled body/rotor flapping and lead-lag dynamics in the identification model structure to allow the accurate prediction of control system bandwidth limitations. Lower-order models are useful for estimating nominal control system performance only when the flight data used for the identification are band-limited to be consistent with the frequency range of applicability of the model. The flight test results presented in this paper are consistent with theoretical studies by previous researchers.
Tischler, Mark B.↗
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↗
System identification requirements for high-bandwidth rotorcraft flight control system design
The application of system identification methods to high-bandwidth rotorcraft flight control system design is examined. Flight test and modeling requirements are illustrated using flight test data from a BO-105 hingeless rotor helicopter. The proposed approach involves the identification of nonparametric (transfer function and state space) model identification. Results for the BO-105 show the need for including coupled body/rotor flapping and lead-lag dynamics in the identification model structure to allow the accurate prediction of control ssytem bandwidth limitations.
Tischler, Mark B.↗
Direct nonparametric multimessenger constraints on the equation of state of cold dense nuclear matter
We utilize the now substantial amount of astrophysical observations of neutron stars (NSs), along with perturbative quantum chromodynamics (pQCD) calculations at high density, to directly constrain the NS equation of state (EOS). To this end, we construct nonparametric EOS priors by using Gaussian processes trained on 75 EOSs, which include models with either hadrons, hyperons, or quarks at high densities. We create a prior using the full EOS sample (model agnostic), and one prior for each EOS family to test model discrimination. We introduce a novel inference approach, which allows the simultaneous sampling of intrinsic and extrinsic parameters of binary NS mergers, as well as a nonparametric equation of state. We showcase this method in a Bayesian updating scheme by first performing a complete analysis of the binary NS merger event GW170817 with minimal assumptions, and sequentially adding information from x-ray and radio NS observations, along with pQCD calculations. Besides providing standard constraints, such as the pressure at twice nuclear saturation density 𝑝(2𝜌 sat ) = 4.3$^{+0.6}_{−0.6}$ × 10 34 dyne/cm 2 , at 95% confidence level, for the model agnostic prior, our methodology shows how the choice of EOS families used in conditioning changes the inferred astrophysical properties of the EOS, namely tidal deformability and maximum supported NS mass. We find hyperonic priors predicting higher tidal deformabilities for a 1.4𝑀 ⊙ NS, and hadronic priors being preferred by the considered astrophysical data.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Gradient-based Optimization for Regression in the Functional Tensor-Train Format
We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of gradient-based optimization procedures, including stochastic gradient descent and quasi-Newton methods, for learning the parameters of a functional tensor-train (FT) that yields improved accuracy over standard alternating least squares methods. The functional tensor-train uses the tensor-train (TT) representation of low-rank arrays as an ansatz for a class of low-multilinear-rank functions. The FT is represented by a set of matrix-valued functions that contain a set of univariate functions, and the regression task is to learn the parameters of these univariate functions. Our second contribution demonstrates that using nonlinearly parameterized univariate functions, e.g., symmetric kernels with moving centers, within each core can outperform the standard approach of using a linear expansion of basis functions. Our final contributions are new rank adaptation and group-sparsity regularization procedures to minimize overfitting. We use several benchmark problems to demonstrate at least an order of magnitude lower accuracy with gradient-based optimization methods than ALS in the low-sample number regime. We also demonstrate an order of magnitude reduction in accuracy on a test problem resulting from nonlinear parameterizations over linear parameterizations. Finally we compare regression performance with 22 other nonparametric and parametric regression methods on 10 real-world data sets. We achieve top-five accuracy for seven of the data sets and best accuracy for two of the data sets. These rankings are the best amongst parametric models and competetive with the best non-parametric methods.
97 MATHEMATICS AND COMPUTING↗
Normative Ranges for Oculomotor and Reaction Time Tests in U.S. Military Service Members and Veterans
AbstractBackground Oculomotor and reaction time tests are frequently used assessments of vestibular symptoms, traumatic brain injury (TBI), or other neurological disorders in both clinical and research contexts. When interpreting these tests it is important to have a reference interval (RI) as a comparison for what constitutes a typical/expected response; however, the current body of research has only limited information regarding normative ranges calculated according to established standards or for a military-specific sample.Purpose The purpose of the present study was to describe RIs for oculomotor and reaction time tests in a cohort of service members and veterans (SMVs) for use as comparators by clinicians and scientists.Research Design Descriptive.Study Sample Participants were prospectively enrolled in the Defense and Veterans Brain Injury Center-Traumatic Brain Injury Center of Excellence 15-year Longitudinal Traumatic Brain Injury Study. Only SMVs without a history of TBI or blast exposure were included in the RI calculations.Data Collection and Analysis The test paradigms included in this analysis were: smooth pursuit, prosaccades, antisaccades, saccades and reaction time, predictive saccades, optokinetic nystagmus, auditory reaction time, and visual reaction time. Nonparametric methods, based on the U.S. Food and Drug Administration's recognized consensus standards, were used to calculate 95% RIs. A comparison between the calculated RIs and those available from previously published research is provided.Results Summary statistics and RIs were calculated for 47 outcome parameters from 13 oculomotor and reaction time tests. Sample sizes and age ranges varied across outcome parameters depending on the availability of reference values for RI calculations. The sample sizes used to calculate RIs ranged from 51 to 69. The age of SMVs included in each RI ranged from 19 to 61 years with mean ages ranging from 37 to 39 years. Similarities/differences between the RIs in the present study and those in previously published research are highly dependent on the outcome parameter; however, in general, the RIs in the present study tended to be somewhat wider.Conclusion The RIs provided in this paper can serve as comparisons for clinicians and scientists who are utilizing these oculomotor and reaction time testing paradigms in similar cohorts of patients or research participants.
Audiology & Speech-Language Pathology↗
Unveiling the effect of composition on nuclear waste immobilization glasses’ durability by nonparametric machine learning
Abstract Ensuring the long-term chemical durability of glasses is critical for nuclear waste immobilization operations. Durable glasses usually undergo qualification for disposal based on their response to standardized tests such as the product consistency test or the vapor hydration test (VHT). The VHT uses elevated temperature and water vapor to accelerate glass alteration and the formation of secondary phases. Understanding the relationship between glass composition and VHT response is of fundamental and practical interest. However, this relationship is complex, non-linear, and sometimes fairly variable, posing challenges in identifying the distinct effect of individual oxides on VHT response. Here, we leverage a dataset comprising 654 Hanford low-activity waste (LAW) glasses across a wide compositional envelope and employ various machine learning techniques to explore this relationship. We find that Gaussian process regression (GPR), a nonparametric regression method, yields the highest predictive accuracy. By utilizing the trained model, we discern the influence of each oxide on the glasses’ VHT response. Moreover, we discuss the trade-off between underfitting and overfitting for extrapolating the material performance in the context of sparse and heterogeneous datasets.
36 MATERIALS SCIENCE↗
Recovering the Star Formation Histories of Recently Quenched Galaxies: The Impact of Model and Prior Choices
Accurate models of the star formation histories (SFHs) of recently quenched galaxies can provide constraints on when and how galaxies shut down their star formation. The recent development of nonparametric SFH models promises the flexibility required to make these measurements. However, model and prior choices significantly affect derived SFHs, particularly for post-starburst galaxies (PSBs), which have sharp changes in their recent SFH. In this paper, we create mock PSBs, then use the Prospector SED fitting software to test how well four different SFH models recover key properties. We find that a two-component parametric model performs well for our simple mock galaxies, but is sensitive to model mismatches. The fixed- and flexible-bin nonparametric models included in Prospector are able to rapidly quench a major burst of star formation, but systematically underestimate the post-burst age by up to 200 Myr. We develop a custom SFH model that allows for additional flexibility in the recent SFH. Our flexible nonparametric model is able to constrain post-burst ages with no significant offset and just ~90 Myr of scatter. Our results suggest that while standard nonparametric models are able to recover first-order quantities of the SFH (mass, SFR, average age), accurately recovering higher-order quantities (burst fraction, quenching time) requires careful consideration of model flexibility. These mock recovery tests are a critical part of future SFH studies. Finally, we show that our new, public SFH model is able to accurately recover the properties of mock star-forming and quiescent galaxies and is suitable for broader use in the SED fitting community. https://github.com/bd-j/prospector
79 ASTRONOMY AND ASTROPHYSICS↗
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.↗
Binomial Test Method for Determining Probability of Detection Capability for Fracture Critical Applications
The capability of an inspection system is established by applications of various methodologies to determine the probability of detection (POD). One accepted metric of an adequate inspection system is that for a minimum flaw size and all greater flaw sizes, there is 0.90 probability of detection with 95% confidence (90/95 POD). Directed design of experiments for probability of detection (DOEPOD) has been developed to provide an efficient and accurate methodology that yields estimates of POD and confidence bounds for both Hit-Miss or signal amplitude testing, where signal amplitudes are reduced to Hit-Miss by using a signal threshold Directed DOEPOD uses a nonparametric approach for the analysis or inspection data that does require any assumptions about the particular functional form of a POD function. The DOEPOD procedure identifies, for a given sample set whether or not the minimum requirement of 0.90 probability of detection with 95% confidence is demonstrated for a minimum flaw size and for all greater flaw sizes (90/95 POD). The DOEPOD procedures are sequentially executed in order to minimize the number of samples needed to demonstrate that there is a 90/95 POD lower confidence bound at a given flaw size and that the POD is monotonic for flaw sizes exceeding that 90/95 POD flaw size. The conservativeness of the DOEPOD methodology results is discussed. Validated guidelines for binomial estimation of POD for fracture critical inspection are established.
Generazio, Edward R.↗