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Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding
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Evaluation of Temperature Trends from MW+IR Sounders, GPS-RO and Reanalysis Using Nonparametric Multivariate Regression Techniques
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A Nonparametric Statistical Technique for Spatial Downscaling of Precipitation over High Mountain Asia
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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.
Decision boundary feature selection for non-parametric classifier
Feature selection has been one of the most important topics in pattern recognition. Although many authors have studied feature selection for parametric classifiers, few algorithms are available for feature selection for nonparametric classifiers. In this paper we propose a new feature selection algorithm based on decision boundaries for nonparametric classifiers. We first note that feature selection for pattern recognition is equivalent to retaining 'discriminantly informative features', and a discriminantly informative feature is related to the decision boundary. A procedure to extract discriminantly informative features based on a decision boundary for nonparametric classification is proposed. Experiments show that the proposed algorithm finds effective features for the nonparametric classifier with Parzen density estimation.
Geometric analysis and restitution of digital multispectral scanner data arrays
An investigation was conducted to define causes of geometric defects within digital multispectral scanner (MSS) data arrays, to analyze the resulting geometric errors, and to investigate restitution methods to correct or reduce these errors. Geometric transformation relationships for scanned data, from which collinearity equations may be derived, served as the basis of parametric methods of analysis and restitution of MSS digital data arrays. The linearization of these collinearity equations is presented. Algorithms considered for use in analysis and restitution included the MSS collinearity equations, piecewise polynomials based on linearized collinearity equations, and nonparametric algorithms. A proposed system for geometric analysis and restitution of MSS digital data arrays was used to evaluate these algorithms, utilizing actual MSS data arrays. It was shown that collinearity equations and nonparametric algorithms both yield acceptable results, but nonparametric algorithms possess definite advantages in computational efficiency. Piecewise polynomials were found to yield inferior results.
Application of parametric and non-parametric statistics to sounding rocket dispersion including large sample and small sample theory
Analytical methods for obtaining large and small samples to be used in sounding rocket dispersion statistics are described. When the distribution of the parent population is assumed known, a method is called parametric. When no assumption is made about the parent population, the method is called nonparametric. Parametric and nonparametric methods are given for both large and small samples. The assumed distribution for the parametric case will be normal and it is shown that sample nonparametric theory is easier to apply in many cases, giving essentially the same results as parametric theory. The method is applied to the dispersion of NASA sounding rockets from 1959 to 1974.
A neural network approach to cloud classification
It is shown that, using high-spatial-resolution data, very high cloud classification accuracies can be obtained with a neural network approach. A texture-based neural network classifier using only single-channel visible Landsat MSS imagery achieves an overall cloud identification accuracy of 93 percent. Cirrus can be distinguished from boundary layer cloudiness with an accuracy of 96 percent, without the use of an infrared channel. Stratocumulus is retrieved with an accuracy of 92 percent, cumulus at 90 percent. The use of the neural network does not improve cirrus classification accuracy. Rather, its main effect is in the improved separation between stratocumulus and cumulus cloudiness. While most cloud classification algorithms rely on linear parametric schemes, the present study is based on a nonlinear, nonparametric four-layer neural network approach. A three-layer neural network architecture, the nonparametric K-nearest neighbor approach, and the linear stepwise discriminant analysis procedure are compared. A significant finding is that significantly higher accuracies are attained with the nonparametric approaches using only 20 percent of the database as training data, compared to 67 percent of the database in the linear approach.
On the estimation of climatological Z-R relationships
A statistical framework for climatological Z-R parameter estimation is developed and simulation experiments are conducted to examine sampling properties of the estimators. Both parametric and nonparametric models are considered. For parametric models, it is shown that Z-R parameters can be estimated by maximum likelihood, a procedure with optimal large sample properties. A general nonparametric framework for climatological Z-R estimation is also developed. Nonparametric procedures are attractive because of their flexibility in dealing with certain types of measurement errors common to radar data. Simulation experiments show that even under favorable assumptions on error characteristics of radar and raingages, large datasets are required to obtain accurate Z-R parameter estimates. Another important conclusion is that estimation results are generally quite sensitive to radar and raingage measurement thresholds. For fixed sample size, the simulation results can be used to provide quantitative assessments of the accuracy of Z-R model parameter estimates. These results are particularly useful for error analysis of precipitation products that are derived using climatological Z-R relations. One example is the large-area rainfall estimates derived using the height-area rainfall threshold (HART) technique.
Extended dark energy analysis using DESI DR2 BAO measurements
We conduct an extended analysis of dark energy constraints, in support of the findings of the Dark Energy Spectroscopic Instrument (DESI) second data release cosmology key paper, including DESI data, Planck cosmic microwave background observations, and three different supernova compilations. Using a broad range of parametric and nonparametric methods, we explore the dark energy phenomenology and find consistent trends across all approaches, in good agreement with the 𝑤 0 𝑤 𝑎 CDM (cold dark matter) key paper results. Even with the additional flexibility introduced by nonparametric approaches, such as binning and Gaussian processes, we find that extending Λ CDM to include a two-parameter 𝑤(𝑧) is sufficient to capture the trends present in the data. Finally, we examine three dark energy classes with distinct dynamics, including quintessence scenarios satisfying 𝑤 ≥ −1, to explore what underlying physics can explain such deviations. The current data indicate a clear preference for models that feature a phantom crossing; although alternatives lacking this feature are disfavored, they cannot yet be ruled out. Our analysis confirms that the evidence for dynamical dark energy, particularly at low redshift (𝑧 ≲ 0.3), is robust and stable under different modeling choices.
Flux Cube Reconstruction from Slitless Spectroscopy
Slitless spectroscopy enables efficient, large-area surveys without target preselection, yet it faces challenges from source blending, higher noise, and lost spatial–spectral information. We present an advanced, nonparametric, data-driven algorithm that leverages multiple dispersion angles to reconstruct three-dimensional flux distributions, providing low-resolution integral field unit capabilities from slitless data. By treating each pixel as an independent element, our method naturally handles source confusion without requiring prior assumptions regarding redshifts, templates, or model libraries. We validate the algorithm using simulated Roman Space Telescope wide-field slitless spectroscopy images that are equivalent to what is expected from the High-Latitude Time-Domain Survey. First, we demonstrate that a host-galaxy model reconstructed from multiple dispersion angles can be used to accurately subtract host light from a transient, recovering a Type Ia supernova spectrum with minimal bias. Second, we showcase a high-fidelity flux-cube reconstruction of a complex galaxy, successfully measuring the redshift and recovering continuum, emission, and absorption features. This approach highlights the potential of multi-dispersion-angle slitless data to provide spatially resolved spectral information in a nonparametric way, which is traditionally accessible only with integral field spectroscopy, opening a new window into large, unbiased, and spatially resolved studies of galaxy evolution.
Minimum distance classification in remote sensing
The utilization of minimum distance classification methods in remote sensing problems, such as crop species identification, is considered. Literature concerning both minimum distance classification problems and distance measures is reviewed. Experimental results are presented for several examples. The objective of these examples is to: (a) compare the sample classification accuracy of a minimum distance classifier, with the vector classification accuracy of a maximum likelihood classifier, and (b) compare the accuracy of a parametric minimum distance classifier with that of a nonparametric one. Results show the minimum distance classifier performance is 5% to 10% better than that of the maximum likelihood classifier. The nonparametric classifier is only slightly better than the parametric version.
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.
Design of adaptive control systems by means of self-adjusting transversal filters
The design of closed-loop adaptive control systems based on nonparametric identification was addressed. Implementation is by self-adjusting Least Mean Square (LMS) transversal filters. The design concept is Model Reference Adaptive Control (MRAC). Major issues are to preserve the linearity of the error equations of each LMS filter, and to prevent estimation bias that is due to process or measurement noise, thus providing necessary conditions for the convergence and stability of the control system. The controlled element is assumed to be asymptotically stable and minimum phase. Because of the nonparametric Finite Impulse Response (FIR) estimates provided by the LMS filters, a-priori information on the plant model is needed only in broad terms. Following a survey of control system configurations and filter design considerations, system implementation is shown here in Single Input Single Output (SISO) format which is readily extendable to multivariable forms. In extensive computer simulation studies the controlled element is represented by a second-order system with widely varying damping, natural frequency, and relative degree.
A linear programming approach to characterizing norm bounded uncertainty from experimental data
The linear programming spectral overbounding and factorization (LPSOF) algorithm, an algorithm for finding a minimum phase transfer function of specified order whose magnitude tightly overbounds a specified nonparametric function of frequency, is introduced. This method has direct application to transforming nonparametric uncertainty bounds (available from system identification experiments) into parametric representations required for modern robust control design software (i.e., a minimum-phase transfer function multiplied by a norm-bounded perturbation).
Are the 1986-1988 changes in solar free-oscillation frequency splitting significant?
The solar normal-mode splitting coefficients deduced from Big Bear Solar Observatory (BBSO) data differ between 1986 and 1988; inversions for equatorial rotation are slower at depth and faster near the surface in 1988 than in 1986. The significance of the change has been disputed. The data sets overlap for five splitting coefficients (a(j))super 5 sub j = 1 associated with 710 multiplets. On the assumption that rotation rate varies smoothly with radius, both data sets are satisfied by the same rotation model at all colatitudes except near 30-40 deg and near 70 deg (and at their southern hemisphere reflections 140-150 deg and 110 deg). The evidence for equatorial change is weak. Nonparametric tests show a significant offset in the magnitudes of a(1), a(2), and a(4), and of linear combinations sensitive to rotation at colatitudes of 60-80 deg (and 120 deg). Nonparametric tests show significant radial trends in the changes to a(2), a(4), and (less significantly) a(5). There is strong anticorrelation between a(2) and a(4), a(1) and a(3), and a(3) and a(5), suggesting that the estimates are not independent. Individual coefficients a(j) show more evidence for change than do 'physical' linear combinations, adding weight to this hypothesis. Some of the changes in splitting might be related to solar activity, which changed most near colatitude 70 deg from 1986 to 1988.
Hidden Markov models and neural networks for fault detection in dynamic systems
Neural networks plus hidden Markov models (HMM) can provide excellent detection and false alarm rate performance in fault detection applications, as shown in this viewgraph presentation. Modified models allow for novelty detection. Key contributions of neural network models are: (1) excellent nonparametric discrimination capability; (2) a good estimator of posterior state probabilities, even in high dimensions, and thus can be embedded within overall probabilistic model (HMM); and (3) simple to implement compared to other nonparametric models. Neural network/HMM monitoring model is currently being integrated with the new Deep Space Network (DSN) antenna controller software and will be on-line monitoring a new DSN 34-m antenna (DSS-24) by July, 1994.