Stability in signal detection problems.
Stability in signal detection and measurement based on statistical inference made from values of functional on sample space
STATISTICAL COMMUNICATION THEORY↗
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An early estimate for the size of cycle 23
The maximum amplitude for the next sunspot cycle is estimated on the basis of inferred statistical trends and associations from the last 12 cycles. Specific attention is given to the extrapolation of the inferred long-term upward trend against time of the maximum amplitude RM which is the maximum value of the smoothed sunspot number for a given cycle. Also examined in depth are the apparent inherent differences found in even- and odd-numbered sunspot cycles. RM is plotted vs cycle number, and RM is plotted against RM for odd-following cycle pairs. RM values are shown to be greater than 110.6 for six of the last six sunspot cycles, and the trend suggests that cycle 23 should have RM of more than 150 particularly in light of the fact that the odd-following cycle is always larger than the even cycle. Evidence is shown to predict an RM of at least 176.4, making cycle 23 one of the largest of the modern era.
Wilson, Robert M.↗
Modular Spectral Inference Framework Applied to Young Stars and Brown Dwarfs
In practice, synthetic spectral models are imperfect, causing inaccurate estimates of stellar parameters. Using forward modeling and statistical inference, we derive accurate stellar parameters for a given observed spectrum by emulating a grid of precomputed spectra to track uncertainties. Spectral inference as applied to brown dwarfs re: Synthetic spectral models (Marley et al 1996 and 2014) via the newest grid spans a massive multi-dimensional grid applied to IGRINS spectra, improving atmospheric models for JWST. When applied to young stars(10Myr) with large starpots, they can be measured spectroscopically, especially in the near-IR with IGRINS.
K↗
Use of Minute-by-Minute Cardiovascular Measurements During Tilt Tests to Strengthen Inference on the Effect of Long-Duration Space Flight on Orthostatic Hypotension
Typical methodology for evaluating the effects of spaceflight on orthostatic hypotension (OH) has been survival analysis of tolerance times from 80 head-up tilt tests. However when scheduled test durations are short, there may not be enough failures to allow survival analysis to adequately estimate and compare the effects of flight phase (e.g. pre-flight, number of days post-flight), flight duration, and their interaction, as well as interactions with effects of interventions or countermeasures. The problem is exacerbated in the presence of a repeated measures design, in which subjects participate in tilt tests during various flight phases. Here we show how it is possible to dramatically improve the efficiency of statistical inference in this setting by making use of the additional information contained in minute-by-minute observations of cardiovascular parameters thought to be reflective of progression towards presyncope during tilt testing. Methods: We retrospectively examined operational tilt test (OTT; 10 -min 80 head-up tilt) data from 20 International Space Station (ISS) and 66 Shuttle astronauts 10 d before launch (L-10), on landing day (R+0) and during recovery (R+1, R+3, R+6-10) depending on the level of participation. Data from 5 ISS astronauts tested on R+0 or R+1 who used non-standard countermeasures were excluded. In addition to OTT survival time, 8 cardiovascular parameters (CP: heart rate, systolic, diastolic, and mean arterial blood pressure, pulse pressure, stroke volume, cardiac output, and total peripheral resistance) that might be predictive of progression towards presyncope were measured every minute of each OTT. Statistical analysis was predicated on a two ]stage model of causation. In the first stage, flight duration and time from landing affect the astronauts' degree of OH, which is manifested in the time trends and variation of the above CPs during OTTs. In the second stage, the behavior of these parameters directly affects OTT survival time. Actual analysis proceeded in the opposite direction. First we identified those CPs or linear combinations that best predicted OTT survival regardless of what spaceflight conditions led to OTT completion or presyncope. From these, we calculated a summary statistic (one per OTT) that best predicted survival. We then used mixed ]model regression analysis to relate changes in the summary statistic to flight phase and duration. Inference on the effects of phase, duration, and their interaction on OH follows directly from this second analysis. Results: A linear combination (W) of diastolic blood pressure (DBP) and stroke volume (SV) was found to be the best predictor of OTT survival using the complete data set of minute-by-minute observations of CPs for each OTT. Furthermore, the log-transformed standard deviation of W (Z = log SW) was found to be a strong predictor of survival in the reduced data set consisting of one observation per OTT. In other words, this measure of variability of W during an OTT was the best indicator of whether or not the subject could complete the 10-min test, with higher variability (i.e. higher values of Z) being associated with greater probability of failure. In the mixed-model regression analysis where Z was now treated as a outcome with flight phase and duration groups (ISS and STS) as predictors, we found that there was a significantly more variability in W (higher values of Z) for both groups at R+0, but with no evidence of an interaction until R+3, when the ISS group still had inflated variability, but not the STS group. Conclusions: Variability of the cardiovascular index W recovers more slowly after long-compared to short-duration spaceflight. Since high variability of W has also been shown to be predictive of OTT failure, a primary manifestation of OH, a logical conclusion is that recovery from OH also is slower after long-duration compared to short-duration spaceflights.
Feiveson, Alan H.↗
Gaussian statistics of the cosmic microwave background: Correlation of temperature extrema in the COBE DMR two-year sky maps
We use the two-point correlation function of the extrema points (peaks and valleys) in the Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) 2 year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background anisotropy. A maximum-likelihood analysis compares the DMR data to n = 1 toy models whose random-phase spherical harmonic components a(sub lm) are drawn from either Gaussian, chi-square, or log-normal parent populations. The likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model. There is less than 10% chance that the non-Gaussian models tested describe the DMR data, limited primarily by type II errors in the statistical inference. The extrema correlation function is a stronger test for this class of non-Gaussian models than topological statistics such as the genus.
Kogut, A.↗
Statistical characterization of experimental magnetized liner inertial fusion stagnation images using deep-learning-based fuel–background segmentation
Significant variety is observed in spherical crystal x-ray imager (SCXI) data for the stagnated fuel–liner system created in Magnetized Liner Inertial Fusion (MagLIF) experiments conducted at the Sandia National Laboratories Z-facility. As a result, image analysis tasks involving, e.g., region-of-interest selection (i.e. segmentation), background subtraction and image registration have generally required tedious manual treatment leading to increased risk of irreproducibility, lack of uncertainty quantification and smaller-scale studies using only a fraction of available data. We present a convolutional neural network (CNN)-based pipeline to automate much of the image processing workflow. This tool enabled batch preprocessing of an ensemble of N scans = 139 SCXI images across N exp = 67 different experiments for subsequent study. The pipeline begins by segmenting images into the stagnated fuel and background using a CNN trained on synthetic images generated from a geometric model of a physical three-dimensional plasma. The resulting segmentation allows for a rules-based registration. Our approach flexibly handles rarely occurring artifacts through minimal user input and avoids the need for extensive hand labelling and augmentation of our experimental dataset that would be needed to train an end-to-end pipeline. Here we also fit background pixels using low-degree polynomials, and perform a statistical assessment of the background and noise properties over the entire image database. Our results provide a guide for choices made in statistical inference models using stagnation image data and can be applied in the generation of synthetic datasets with realistic choices of noise statistics and background models used for machine learning tasks in MagLIF data analysis. We anticipate that the method may be readily extended to automate other MagLIF stagnation imaging applications.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Calculating Statistical Orbit Distributions Using GEO Optical Observations with the Michigan Orbital Debris Survey Telescope (MODEST)
NASA's Orbital Debris measurements program has a goal to characterize the small debris environment in the geosynchronous Earth-orbit (GEO) region using optical telescopes ("small" refers to objects too small to catalog and track with current systems). Traditionally, observations of GEO and near-GEO objects involve following the object with the telescope long enough to obtain an orbit suitable for tracking purposes. Telescopes operating in survey mode, however, randomly observe objects that pass through their field of view. Typically, these short-arc observation are inadequate to obtain detailed orbits, but can be used to estimate approximate circular orbit elements (semimajor axis, inclination, and ascending node). From this information, it should be possible to make statistical inferences about the orbital distributions of the GEO population bright enough to be observed by the system. The Michigan Orbital Debris Survey Telescope (MODEST) has been making such statistical surveys of the GEO region for four years. During that time, the telescope has made enough observations in enough areas of the GEO belt to have had nearly complete coverage. That means that almost all objects in all possible orbits in the GEO and near- GEO region had a non-zero chance of being observed. Some regions (such as those near zero inclination) have had good coverage, while others are poorly covered. Nevertheless, it is possible to remove these statistical biases and reconstruct the orbit populations within the limits of sampling error. In this paper, these statistical techniques and assumptions are described, and the techniques are applied to the current MODEST data set to arrive at our best estimate of the GEO orbit population distribution.
Matney, M.↗
Extracting the Breakout Distance from the ECOT Trajectories: Gaussian Process Regression Approach
Enhanced Corner Turning (ECOT) experiments provide an important metric of performance of high explosive (HE) formulations. The breakout distance is a single scalar value that characterizes the corner turning efficiency of an HE. Extracting the breakout distance from the raw ECOT results, whether experimental or simulated, is a conceptually straightforward procedure which, however, is non-unique, especially in the presence of noise. More specifically, this procedure involves numerical smoothing and selecting particular values for parameters of this smoothing introduces human bias. In this work, we propose to use the Gaussian process regression to analyze ECOT results. This analysis involves the effective smoothing of the data, thus allowing for accurate extraction of the breakout distance. Most importantly, the parameters of this smoothing can be inferred from the ECOT data itself, rendering the approach effectively parameter-free and thus diminishing the human bias. An additional benefit of the Gaussian process regression, being a statistical inference method, is that not just the value of the breakout distance, but also its confidence interval can be extracted from the data. This report introduces the Gaussian process regression, as applied to ECOT, and demonstrates its usefulness by extracting the breakout distances for a selection of experimental and simulated data.
45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
A differentiable simulation package for performing inference of synchrotron-radiation-based diagnostics
The direction of particle accelerator development is ever-increasing beam quality, currents and repetition rates. This poses a challenge to traditional diagnostics that directly intercept the beam due to the mutual destruction of both the beam and the diagnostic. An alternative approach is to infer beam parameters non-invasively from the synchrotron radiation emitted in bending magnets. However, inferring the beam distribution from a measured radiation pattern is a complex and computationally expensive task. To address this challenge we present SYRIPY ( SYnchrotron Radiation In PYthon ), a software package intended as a tool for performing inference of synchrotron-radiation-based diagnostics. SYRIPY has been developed using PyTorch , which makes it both differentiable and able to leverage the high performance of GPUs, two vital characteristics for performing statistical inference. The package consists of three modules: a particle tracker, Lienard–Wiechert solver and Fourier optics propagator, allowing start-to-end simulation of synchrotron radiation detection to be carried out. SYRIPY has been benchmarked against SRW , the prevalent numerical package in the field, showing good agreement and up to a 50× speed improvement. Finally, we have demonstrated how SYRIPY can be used to perform Bayesian inference of beam parameters using stochastic variational inference.
43 PARTICLE ACCELERATORS↗
Comparing hard and soft prior bounds in geophysical inverse problems
In linear inversion of a finite-dimensional data vector y to estimate a finite-dimensional prediction vector z, prior information about X sub E is essential if y is to supply useful limits for z. The one exception occurs when all the prediction functionals are linear combinations of the data functionals. Two forms of prior information are compared: a soft bound on X sub E is a probability distribution p sub x on X which describeds the observer's opinion about where X sub E is likely to be in X; a hard bound on X sub E is an inequality Q sub x(X sub E, X sub E) is equal to or less than 1, where Q sub x is a positive definite quadratic form on X. A hard bound Q sub x can be softened to many different probability distributions p sub x, but all these p sub x's carry much new information about X sub E which is absent from Q sub x, and some information which contradicts Q sub x. Both stochastic inversion (SI) and Bayesian inference (BI) estimate z from y and a soft prior bound p sub x. If that probability distribution was obtained by softening a hard prior bound Q sub x, rather than by objective statistical inference independent of y, then p sub x contains so much unsupported new information absent from Q sub x that conclusions about z obtained with SI or BI would seen to be suspect.
Backus, George E.↗
Comparing hard and soft prior bounds in geophysical inverse problems
In linear inversion of a finite-dimensional data vector y to estimate a finite-dimensional prediction vector z, prior information about X sub E is essential if y is to supply useful limits for z. The one exception occurs when all the prediction functionals are linear combinations of the data functionals. Two forms of prior information are compared: a soft bound on X sub E is a probability distribution p sub x on X which describes the observer's opinion about where X sub E is likely to be in X; a hard bound on X sub E is an inequality Q sub x(X sub E, X sub E) is equal to or less than 1, where Q sub x is a positive definite quadratic form on X. A hard bound Q sub x can be softened to many different probability distributions p sub x, but all these p sub x's carry much new information about X sub E which is absent from Q sub x, and some information which contradicts Q sub x. Both stochastic inversion (SI) and Bayesian inference (BI) estimate z from y and a soft prior bound p sub x. If that probability distribution was obtained by softening a hard prior bound Q sub x, rather than by objective statistical inference independent of y, then p sub x contains so much unsupported new information absent from Q sub x that conclusions about z obtained with SI or BI would seen to be suspect.
Backus, George E.↗
Inference for Nonparanormal Partial Correlation via Regularized Rank-Based Nodewise Regression
Abstract Partial correlation is a common tool in studying conditional dependence for Gaussian distributed data. However, partial correlation being zero may not be equivalent to conditional independence under non-Gaussian distributions. In this paper, we propose a statistical inference procedure for partial correlations under the high-dimensional nonparanormal (NPN) model where the observed data are normally distributed after certain monotone transformations. The NPN partial correlation is the partial correlation of the normal transformed data under the NPN model, which is a more general measure of conditional dependence. We estimate the NPN partial correlations by regularized nodewise regression based on the empirical ranks of the original data. A multiple testing procedure is proposed to identify the nonzero NPN partial correlations. The proposed method can be carried out by a simple coordinate descent algorithm for lasso optimization. It is easy-to-implement and computationally more efficient compared to the existing methods for estimating NPN graphical models. Theoretical results are developed to show the asymptotic normality of the proposed estimator and to justify the proposed multiple testing procedure. Numerical simulations and a case study on brain imaging data demonstrate the utility of the proposed procedure and evaluate its performance compared to the existing methods. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.
97 MATHEMATICS AND COMPUTING↗
Statistical Aspects of North Atlantic Basin Tropical Cyclones During the Weather Satellite Era, 1960-2013
This Technical Publication (TP) is part 2 of a two-part study of the North Atlantic basin tropical cyclones that occurred during the weather satellite era, 1960-2013. In particular, this TP examines the inferred statistical relationships between 25 tropical cyclone parameters and 9 specific climate-related factors, including the (1) Oceanic Niño Index (ONI), (2) Southern Oscillation Index (SOI), (3) Atlantic Multidecadal Oscillation (AMO) index, (4) Quasi-Biennial Oscillation (QBO) index, (5) North Atlantic Oscillation (NAO) index of the Climate Prediction Center (CPC), (6) NAO index of the Climate Research Unit (CRU), (7) Armagh surface air temperature (ASAT), (8) Global Land-Ocean Temperature Index (GLOTI), and (9) Mauna Loa carbon dioxide (CO2) (MLCO2) index. Part 1 of this two-part study examined the statistical aspects of the 25 tropical cyclone parameters (e.g., frequencies, peak wind speed (PWS), accumulated cyclone energy (ACE), etc.) and provided the results of statistical testing (i.e., runs-testing, the t-statistic for independent samples, and Poisson distributions). Also, the study gave predictions for the frequencies of the number of tropical cyclones (NTC), number of hurricanes (NH), number of major hurricanes (NMH), and number of United States land-falling hurricanes (NUSLFH) expected for the 2014 season, based on the statistics of the overall interval 1960-2013, the subinterval 1995-2013, and whether the year 2014 would be either an El Niño year (ENY) or a non-El Niño year (NENY).
Wilson, Robert M.↗
Topological Interpretability for Deep Learning
With the growing adoption of AI-based systems across everyday life, the need to understand their decision-making mechanisms is correspondingly increasing. The level at which we can trust the statistical inferences made from AI-based decision systems is an increasing concern, especially in high-risk systems such as criminal justice or medical diagnosis, where incorrect inferences may have tragic consequences. Despite their successes in providing solutions to problems involving real-world data, deep learning (DL) models cannot quantify the certainty of their predictions. These models are frequently quite confident, even when their solutions are incorrect. This work presents a method to infer prominent features in two DL classification models trained on clinical and non-clinical text by employing techniques from topological and geometric data analysis. We create a graph of a model's feature space and cluster the inputs into the graph's vertices by the similarity of features and prediction statistics. We then extract subgraphs demonstrating high-predictive accuracy for a given label. These subgraphs contain a wealth of information about features that the DL model has recognized as relevant to its decisions. We infer these features for a given label using a distance metric between probability measures, and demonstrate the stability of our method compared to the LIME and SHAP interpretability methods. This work establishes that we may gain insights into the decision mechanism of a DL model. This method allows us to ascertain if the model is making its decisions based on information germane to the problem or identifies extraneous patterns within the data.
Spannaus, Adam↗
Modeling of LEO Orbital Debris Populations in Centimeter and Millimeter Size Regimes
The building of the NASA Orbital Debris Engineering Model, whether ORDEM2000 or its recently updated version ORDEM2010, uses as its foundation a number of model debris populations, each truncated at a minimum object-size ranging from 10 micron to 1 m. This paper discusses the development of the ORDEM2010 model debris populations in LEO (low Earth orbit), focusing on centimeter (smaller than 10 cm) and millimeter size regimes. Primary data sets used in the statistical derivation of the cm- and mm-size model populations are from the Haystack radar operated in a staring mode. Unlike cataloged objects of sizes greater than approximately 10 cm, ground-based radars monitor smaller-size debris only in a statistical manner instead of tracking every piece. The mono-static Haystack radar can detect debris as small as approximately 5 mm at moderate LEO altitudes. Estimation of millimeter debris populations (for objects smaller than approximately 6 mm) rests largely on Goldstone radar measurements. The bi-static Goldstone radar can detect 2- to 3-mm objects. The modeling of the cm- and mm-debris populations follows the general approach to developing other ORDEM2010-required model populations for various components and types of debris. It relies on appropriate reference populations to provide necessary prior information on the orbital structures and other important characteristics of the debris objects. NASA's LEO-to-GEO Environment Debris (LEGEND) model is capable of furnishing such reference populations in the desired size range. A Bayesian statistical inference process, commonly adopted in ORDEM2010 model-population derivations, changes a priori distribution into a posteriori distribution and thus refines the reference populations in terms of data. This paper describes key elements and major steps in the statistical derivations of the cm- and mm-size debris populations and presents results. Due to lack of data for near 1-mm sizes, the model populations of 1- to 3.16-mm objects are an empirical extension from larger debris. The extension takes into account the results of micro-debris (from 10 micron to 1 mm) population modeling that is based on shuttle impact data, in the hope of making a smooth transition between micron and millimeter size regimes. This paper also includes a brief discussion on issues and potential future work concerning the analysis and interpretation of Goldstone radar data.
Xu, Y.-L.↗
Data Analysis with Graphical Models: Software Tools
Probabilistic graphical models (directed and undirected Markov fields, and combined in chain graphs) are used widely in expert systems, image processing and other areas as a framework for representing and reasoning with probabilities. They come with corresponding algorithms for performing probabilistic inference. This paper discusses an extension to these models by Spiegelhalter and Gilks, plates, used to graphically model the notion of a sample. This offers a graphical specification language for representing data analysis problems. When combined with general methods for statistical inference, this also offers a unifying framework for prototyping and/or generating data analysis algorithms from graphical specifications. This paper outlines the framework and then presents some basic tools for the task: a graphical version of the Pitman-Koopman Theorem for the exponential family, problem decomposition, and the calculation of exact Bayes factors. Other tools already developed, such as automatic differentiation, Gibbs sampling, and use of the EM algorithm, make this a broad basis for the generation of data analysis software.
Buntine, Wray L.↗
Experimental control in software reliability certification
There is growing interest in software 'certification', i.e., confirmation that software has performed satisfactorily under a defined certification protocol. Regulatory agencies, customers, and prospective reusers all want assurance that a defined product standard has been met. In other industries, products are typically certified under protocols in which random samples of the product are drawn, tests characteristic of operational use are applied, analytical or statistical inferences are made, and products meeting a standard are 'certified' as fit for use. A warranty statement is often issued upon satisfactory completion of a certification protocol. This paper outlines specific engineering practices that must be used to preserve the validity of the statistical certification testing protocol. The assumptions associated with a statistical experiment are given, and their implications for statistical testing of software are described.
Trammell, Carmen J.↗
Computational Inference of Vibratory System with Incomplete Modal Information Using Parallel, Interactive and Adaptive Markov Chains
Inverse analysis of vibratory system is an important subject in fault identification, model updating, and robust design and control. It is challenging subject because 1) the problem is oftentimes underdetermined while the measurements are limited and/or incomplete; 2) many combinations of parameters may yield results that are similar with respect to actual response measurements; and 3) uncertainties inevitably exist. The aim of this research is to leverage upon computational intelligence through statistical inference to facilitate an enhanced, probabilistic framework using incomplete modal response measurement. This new framework is built upon efficient inverse identification through optimization, whereas Bayesian inference is employed to account for the effect of uncertainties. To overcome the computational cost barrier, we adopt Markov chain Monte Carlo (MCMC) to characterize the target function/distribution. Instead of using single Markov chain in conventional Bayesian approach, we develop a new sampling theory with multiple parallel, interactive and adaptive Markov chains and incorporate it into Bayesian inference. This can harness the collective power of these Markov chains to realize the concurrent search of multiple local optima. The number of required Markov chains and their respective initial model parameters are automatically determined via Monte Carlo simulation-based sample pre-screening followed by K-means clustering analysis. These enhancements can effectively address the aforementioned challenges in finite element inverse analysis. The validity of this framework is systematically demonstrated through case studies.
K Zhou↗