Search

Over the past decade, a variety of innovative methodologies have been developed to better characterize the relationships between processing conditions and the physical, morphological, and chemical features of special nuclear material (SNM). Different processing conditions generate SNM products with different features, which are known as "signatures" because they are indicative of the processing conditions used to produce the material. These signatures can potentially allow a forensic analyst to determine which processes were used to produce the SNM and make inferences about where the material originated. This article investigates a statistical technique for relating processing conditions to themorphological features of PuO2 particles. We develop a Bayesian implementation of seemingly unrelated regression (SUR) to inverse-predict unknown PuO2 processing conditions from known PuO2 features. Model results from simulated data demonstrate the usefulness of the technique. Applied to empirical data from a bench-scale experiment specifically designed with inverse prediction in mind, our model successfully predicts nitric acid concentration, while results for Pu concentration and precipitation temperature were equivalent to a simple mean model. Our technique compliments other recent methodologies developed for forensic analysis of nuclear material and can be generalized across the field of chemometrics for application to other materials. [ABSTRACT FROM AUTHOR]

Detecting changepoints in functional data has become an important problem as interest in monitoring of climate phenomenon has increased, where the data is functional in nature. The observed data often contains both amplitude (y$$ y $$‐axis) and phase (x$$ x $$‐axis) variability. If not accounted for properly, true changepoints may be undetected, and the estimated underlying mean change functions will be incorrect. In this article, an elastic functional changepoint method is developed which properly accounts for these types of variability. The method can detect amplitude and phase changepoints which current methods in the literature do not, as they focus solely on the amplitude changepoint. This method can easily be implemented using the functions directly or can be computed via functional principal component analysis to ease the computational burden. We apply the method and its nonelastic competitors to both simulated data and observed data to show its efficiency in handling data with phase variation with both amplitude and phase changepoints. We use the method to evaluate potential changes in stratospheric temperature due to the eruption of Mt. Pinatubo in the Philippines in June 1991. Using an epidemic changepoint model, we find evidence of a increase in stratospheric temperature during a period that contains the immediate aftermath of Mt. Pinatubo, with most detected changepoints occurring in the tropics as expected. [ABSTRACT FROM AUTHOR]

With the recent surge in big data analytics for hyperdimensional data, there is a renewed interest in dimensionality reduction techniques. In order for these methods to improve performance gains and understanding of the underlying data, a proper metric needs to be identified. This step is often overlooked, and metrics are typically chosen without consideration of the underlying geometry of the data. In this paper, we present a method for incorporating elastic metrics into the t‐distributed stochastic neighbour embedding (t‐SNE) and Uniform Manifold Approximation and Projection (UMAP). We apply our method to functional data, which is uniquely characterized by rotations, parameterization and scale. If these properties are ignored, they can lead to incorrect analysis and poor classification performance. Through our method, we demonstrate improved performance on shape identification tasks for three benchmark data sets (MPEG‐7, Car data set and Plane data set of Thankoor), where we achieve 0.77, 0.95 and 1.00 F1 score, respectively. [ABSTRACT FROM AUTHOR]

We develop a method for constructing tolerance bounds for functional data with random warping variability. In particular, we define a generative, probabilistic model for the amplitude and phase components of such observations, which parsimoniously characterizes variability in the baseline data. Based on the proposed model, we define two different types of tolerance bounds that are able to measure both types of variability, and as a result, identify when the data has gone beyond the bounds of amplitude and/or phase. The first functional tolerance bounds are computed via a bootstrap procedure on the geometric space of amplitude and phase functions. The second functional tolerance bounds utilize functional Principal Component Analysis to construct a tolerance factor. This work is motivated by two main applications: process control and disease monitoring. The problem of statistical analysis and modeling of functional data in process control is important in determining when a production has moved beyond a baseline. Similarly, in biomedical applications, doctors use long, approximately periodic signals (such as the electrocardiogram) to diagnose and monitor diseases. In this context, it is desirable to identify abnormalities in these signals. We additionally consider a simulated example to assess our approach and compare it to two existing methods. [ABSTRACT FROM AUTHOR]

We study regression using functional predictors in situations where these functions contains both phase and amplitude variability. In other words, the functions are misaligned due to errors in time measurements, and these errors can significantly degrade both model estimation and prediction performance. The current techniques either ignore the phase variability, or handle it via preprocessing, that is, use an off‐the‐shelf technique for functional alignment and phase removal. We develop a functional principal component regression model which has a comprehensive approach in handling phase and amplitude variability. The model utilizes a mathematical representation of the data known as the square‐root slope function. These functions preserve the L2 norm under warping and are ideally suited for simultaneous estimation of regression and warping parameters. Using both simulated and real‐world data sets, we demonstrate our approach and evaluate its prediction performance relative to current models. In addition, we propose an extension to functional logistic and multinomial logistic regression. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of denoising and classification of SONAR signals observed under compositional noise, i.e., they have been warped randomly along the x-axis. The traditional techniques do not account for such noise and, consequently, cannot provide a robust classification of signals. We apply a recent framework that: 1) uses a distance-based objective function for data alignment and noise reduction; and 2) leads to warping-invariant distances between signals for robust clustering and classification. We use this framework to introduce two distances that can be used for signal classification: a) a y-distance, which is the distance between the aligned signals; and b) an x-distance that measures the amount of warping needed to align the signals. We focus on the task of clustering and classifying objects, using acoustic spectrum (acoustic color), which is complicated by the uncertainties in aspect angles at data collections. Small changes in the aspect angles corrupt signals in a way that amounts to compositional noise. We demonstrate the use of the developed metrics in classification of acoustic color data and highlight improvements in signal classification over current methods. [ABSTRACT FROM AUTHOR]