The X sup 2 statistic and the goodness of fit test
Statistical method for evaluating goodness of fit between data set and theoretical distribution of random variables
Argentiero, P. D.↗
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Using the Bootstrap Method for a Statistical Significance Test of Differences between Summary Histograms
A new method is proposed to compare statistical differences between summary histograms, which are the histograms summed over a large ensemble of individual histograms. It consists of choosing a distance statistic for measuring the difference between summary histograms and using a bootstrap procedure to calculate the statistical significance level. Bootstrapping is an approach to statistical inference that makes few assumptions about the underlying probability distribution that describes the data. Three distance statistics are compared in this study. They are the Euclidean distance, the Jeffries-Matusita distance and the Kuiper distance. The data used in testing the bootstrap method are satellite measurements of cloud systems called cloud objects. Each cloud object is defined as a contiguous region/patch composed of individual footprints or fields of view. A histogram of measured values over footprints is generated for each parameter of each cloud object and then summary histograms are accumulated over all individual histograms in a given cloud-object size category. The results of statistical hypothesis tests using all three distances as test statistics are generally similar, indicating the validity of the proposed method. The Euclidean distance is determined to be most suitable after comparing the statistical tests of several parameters with distinct probability distributions among three cloud-object size categories. Impacts on the statistical significance levels resulting from differences in the total lengths of satellite footprint data between two size categories are also discussed.
Xu, Kuan-Man↗
Detecting differential protein abundance by combining peptide level P -values
The majority of methods for detecting differentially abundant proteins between samples in label-free LC-MS bottom-up proteomics experiments rely on statistically testing inferred protein abundances derived from peptide ionization intensities or averaging peptide level statistics. Here in this paper, we statistically test peptide ionization intensities directly and combine the resulting dependent P-values using the Empirical Brown's Method (EBM), avoiding error introduced through the estimation of protein abundances or summarizing test statistics. We show that on a spike-in proteomics dataset, a peptide level approach using EBM outperforms differential abundance detection using a protein level approach and several analysis workflows, including MSstats. Additionally, we demonstrate the effectiveness of this approach by detecting enriched proteins from an activity-based protein profiling dataset.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Statistics for Testing Under Adverse Conditions
Here we develop a statistical basis for limited adverse testing. This type of testing simultaneously evaluates system performances against minimum requirements and minimizes costs, particularly for large scale engineering projects. Because testing is often expensive and narrow in scope, the data obtained is relatively limited—precisely the opposite of the recent “large data” movement but no less compelling. Although a remarkably common approach for industrial and large-scale government projects, a statistical basis for adverse testing remains poorly explored. Here we prove mathematically, under specific conditions, that setting each independent variable to an adverse condition leads to a similar level of adversity in the dependent variable. For example, setting all normally distributed independent variables to at least their 95th percentile values leads to a result at the 95th percentile. The analysis considers sample size estimates to clarify the value of replicates in this type of testing, determines how many of the independent variables must be set to adverse condition values, and highlights the essential assumptions, so that engineers, statisticians, and subject matter experts know when this statistical framework may be applied successfully.
42 ENGINEERING↗
Statistical Hypothesis Testing in Wavelet Analysis: Theoretical Developments and Applications to Indian Rainfall
Statistical hypothesis tests in wavelet analysis are methods that assess the degree to which a wavelet quantity(e.g., power and coherence) exceeds background noise. Commonly, a point-wise approach is adopted in which a wavelet quantity at every point in a wavelet spectrum is individually compared to the critical level of the point-wise test. However, because adjacent wavelet coefficients are correlated and wavelet spectra often contain many wavelet quantities, the point-wise test can produce many false positive results that occur in clusters or patches. To circumvent the point-wise test drawbacks, it is necessary to implement the recently developed area-wise, geometric, cumulative area-wise, and topological significance tests, which are reviewed and developed in this paper. To improve the computational efficiency of the cumulative area-wise test, a simplified version of the testing procedure is created based on the idea that its output is the mean of individual estimates of statistical significance calculated from the geometric test applied at a set of point-wise significance levels. Ideal examples are used to show that the geometric and cumulative area-wise tests are unable to differentiate wavelet spectral features arising from singularity-like structures from those associated with periodicities. A cumulative arc-wise test is therefore developed to strictly test for periodicities by using normalized arc length, which is defined as the number of points composing a cross section of a patch divided by the wavelet scale in question. A previously proposed topological significance test is formalized using persistent homology profiles (PHPs) measuring the number of patches and holes corresponding to the set of all point-wise significance values. Ideal examples show that the PHPs can be used to distinguish time series containing signal components from those that are purely noise. To demonstrate the practical uses of the existing and newly developed statistical methodologies, a first comprehensive wavelet analysis of Indian rainfall is also provided. An R software package has been written by the author to implement the various testing procedures.
Wind speed↗
Kepler Planet Detection Metrics: Statistical Bootstrap Test
This document describes the data produced by the Statistical Bootstrap Test over the final three Threshold Crossing Event (TCE) deliveries to NExScI: SOC 9.1 (Q1Q16)1 (Tenenbaum et al. 2014), SOC 9.2 (Q1Q17) aka DR242 (Seader et al. 2015), and SOC 9.3 (Q1Q17) aka DR253 (Twicken et al. 2016). The last few years have seen significant improvements in the SOC science data processing pipeline, leading to higher quality light curves and more sensitive transit searches. The statistical bootstrap analysis results presented here and the numerical results archived at NASAs Exoplanet Science Institute (NExScI) bear witness to these software improvements. This document attempts to introduce and describe the main features and differences between these three data sets as a consequence of the software changes.
Bootstrap↗
Earth mover’s distance as a measure of CP violation
We introduce a new unbinned two sample test statistic sensitive to CP violation utilizing the optimal transport plan associated with the Wasserstein (earth mover’s) distance. The efficacy of the test statistic is shown via two examples of CP asymmetric distributions with varying sample sizes: the Dalitz distributions of B 0 → K + π – π 0 and of D 0 → π + π – π 0 decays. The windowed version of the Wasserstein distance test statistic is shown to have comparable sensitivity to CP violation as the commonly used energy test statistic, but also retains information about the localized distributions of CP asymmetry over the Dalitz plot. For large statistic datasets we introduce two modified Wasserstein distance based test statistics — the binned and the sliced Wasserstein distance statistics, which show comparable sensitivity to CP violation, but improved computing time and memory scalings. Finally, general extensions and applications of the introduced statistics are discussed.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Application of a truncated normal failure distribution in reliability testing
Statistical truncated normal distribution function is applied as a time-to-failure distribution function in equipment reliability estimations. Age-dependent characteristics of the truncated function provide a basis for formulating a system of high-reliability testing that effectively merges statistical, engineering, and cost considerations.
Groves, C., Jr.↗
MPACT Safeguards Modeling: FY25 Update
Sandia National Laboratories develops and maintains several open-source software packages to support material accountancy analyses. This includes the Material Accountancy Performance Indicator Toolkit (MAPIT), the Fissile Facility Flow Modeler (F3M) and the Separation and Safeguards Performance Model Library (SSPM-L). MAPIT is responsible for performing statistical safeguards analyses on bulk and itemized data from nuclear fuel cycle facilities and can operate on real or synthetic data. MAPIT is the only open-source software for such analyses. F3M is a library of modules, built in MATLAB Simulink, that contain pre made blocks to represent different generic fuel cycle processes. These blocks can be used together in a modular fashion to represent and simulate nuclear fuel cycle processes with the goal of improving facility-level accountancy during the design phase. F3M is also an open-source library. Finally, the SSPM-L library is a series of completed models built from F3M. The library includes facility models such as a generic PUREX facility and a fuel fabrication facility. The SSPM-L library is not open source, but is available to collaborators with a relevant use case. These tools include modeling and simulation pipelines to simulate nuclear fuel cycle facilities and the underlying software needed to simulate measurement uncertainty and perform statistical analyses. Together, these tools can perform end-to-end nuclear material accountancy analyses. This report documents the various improvements made to these tools in FY25. Specifically, we added new statistical test, new statistical modeling capabilities, new fuel cycle facility models, and launched a new open-source model component library.
97 MATHEMATICS AND COMPUTING↗
Variable loop gain using excessive regeneration for a delayed wide-area control system
Disclosed are methods and systems for adjusting a High Voltage Direct Current (HVDC) compensator output signal to an HVDC system to reduce control loop modulus due to excessive time delay of sensor measurements. Two different time windows, a Short-Time Variance Window (STVW) and an Extended-Time Variance Window (ETVW) may be examined for detection of increased energy. To detect increased energy the HVDC compensator output signal may be passed through a bandpass filter, then variances for the STVW and ETVW may be generated to produce corresponding test statistics. The STVW and ETVW test statistics may be compared to hypothesis test thresholds and have binary logic based on the hypothesis test comparisons used to generate a gain. The gain may then be multiplied times the original HVDC feedback compensator output such that the adjusted HVDC feedback compensator output reduces the control loop modulus when applied to the HVDC system.
Roberson, Dakota↗
Mechanical Impact Testing: A Statistical Measurement
In the decades since the 1950s, when NASA first developed mechanical impact testing of materials, researchers have continued efforts to gain a better understanding of the chemical, mechanical, and thermodynamic nature of the phenomenon. The impact mechanism is a real combustion ignition mechanism that needs understanding in the design of an oxygen system. The use of test data from this test method has been questioned due to lack of a clear method of application of the data and variability found between tests, material batches, and facilities. This effort explores a large database that has accumulated over a number of years and explores its overall nature. Moreover, testing was performed to determine the statistical nature of the test procedure to help establish sample size guidelines for material characterization. The current method of determining a pass/fail criterion based on either light emission or sound report or material charring is questioned.
Engel, Carl D.↗
Data reduction methods, systems, and devices
Systems, methods, and apparatus are disclosed herein for data pattern detection and data reduction. Devices include an input port configured to receive data values that include a plurality of data units. The devices may also include a data analyzer configured to determine a test statistic based on at least some of the plurality of data units, the test statistic indicating a degree of difference between a first data unit and at least a second data unit, the second data unit being received at the input port before the first data unit. The data analyzer includes the first data unit in a first data block responsive to a determination that the test statistic indicates a low degree of difference, the determination being based on a comparison with a designated difference threshold, the first data block being a same data block as a second data block that includes the second data unit.
96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
Statistical significance test for transition matrices of atmospheric Markov chains
Low-frequency variability of large-scale atmospheric dynamics can be represented schematically by a Markov chain of multiple flow regimes. This Markov chain contains useful information for the long-range forecaster, provided that the statistical significance of the associated transition matrix can be reliably tested. Monte Carlo simulation yields a very reliable significance test for the elements of this matrix. The results of this test agree with previously used empirical formulae when each cluster of maps identified as a distinct flow regime is sufficiently large and when they all contain a comparable number of maps. Monte Carlo simulation provides a more reliable way to test the statistical significance of transitions to and from small clusters. It can determine the most likely transitions, as well as the most unlikely ones, with a prescribed level of statistical significance.
Vautard, Robert↗
Cycle life test
Statistical information concerning cell performance characteristics and limitations of secondary spacecraft cells is presented. Weaknesses in cell design as well as battery weaknesses encountered in various satellite programs are reported. Emphasis is placed on improving the reliability of space batteries.
Harkness, J. D.↗
Validation Testing and Statistical Analysis of the Rotary Tumbler Fabric Abrasion Method
The Artemis space suit glove environmental protection garment (EPG) will be the first line of protection used to shield the crewmember’s hands from the environments encountered during extravehicular activity (EVA). As the Artemis missions will include more extreme environments than those experienced on the International Space Station, development, verification, and validation of gloves requires the development of new test methods. A previous paper focused on the development of a test procedure to characterize lunar EVA glove fabrics using ASTM standardized test methods and the design and validation of a new standardized test procedure for comparing abrasion resistance between fabrics using a dust and rock filled rotary tumbler. Preliminary results of testing were presented in that paper. This paper reports on the validation testing and statistical analysis of the newly developed tumbler abrasion test method.
Robert J Jones↗
Eclipse timings of the low-mass X-ray binary EXO 0748-676: Statistical arguments against orbital period changes
EXO 0748-676, an eclipsing low-mass X-ray binary, is one of only about four or five low-mass X-ray binaries for which orbital period evolution has been reported. We observed a single eclipse egress with ROSAT . The time of this egress is consistent with the apparent increase in P(sub orb) previously reported on the basis of EXOSAT and Ginga observations. Standard analysis, in which O-C (observed minus calculated) timing residuals are examined for deviations from a constant period, implicitly assume that the only uncertainty in each residual is measurement error and that these errors are independent. We argue that the variable eclipse durations and profiles observed in EXO 0748-676 imply that there is an additional source of uncertainty in timing measurements, that this uncertainty is intrinsic to the binary system, and that it is correlated from observation to observation with a variance which increases as a function of the number of binary cycles between observations. This intrinsic variability gives rise to spurious trends in O-C residuals which are misinterpreted as changes in the orbital period. We describe several statistics tests which can be used to test for the presence of intrinsic variability. We apply those statistical tests which are suitable to the EXO 0748-676 observations. The apparent changes in the orbital period of EXO 0748-676 can be completely accounted for by intrinsic variability with an rms variability of approximately 0.35 s per orbital cycle. The variability appears to be correlated from cycle-to-cycle on timescales of less than 1 yr. We suggest that the intrinsic variability is related to slow changes in either the source's X-ray luminosity or the structure of the companion star's atmosphere. We note that several other X-ray binaries and cataclysmic variables have previously reported orbital period changes which may also be due to intrinsic variability rather than orbital period evolution.
Hertz, Paul↗
Earth Observing System Covariance Realism
The purpose of covariance realism is to properly size a primary object's covariance in order to add validity to the calculation of the probability of collision. The covariance realism technique in this paper consists of three parts: collection/calculation of definitive state estimates through orbit determination, calculation of covariance realism test statistics at each covariance propagation point, and proper assessment of those test statistics. An empirical cumulative distribution function (ECDF) Goodness-of-Fit (GOF) method is employed to determine if a covariance is properly sized by comparing the empirical distribution of Mahalanobis distance calculations to the hypothesized parent 3-DoF chi-squared distribution. To realistically size a covariance for collision probability calculations, this study uses a state noise compensation algorithm that adds process noise to the definitive epoch covariance to account for uncertainty in the force model. Process noise is added until the GOF tests pass a group significance level threshold. The results of this study indicate that when outliers attributed to persistently high or extreme levels of solar activity are removed, the aforementioned covariance realism compensation method produces a tuned covariance with up to 80 to 90% of the covariance propagation timespan passing (against a 60% minimum passing threshold) the GOF tests-a quite satisfactory and useful result.
Realism↗
Earth Observation System Flight Dynamics System Covariance Realism
This presentation applies a covariance realism technique to the National Aeronautics and Space Administration (NASA) Earth Observation System (EOS) Aqua and Aura spacecraft based on inferential statistics. The technique consists of three parts: collection calculation of definitive state estimates through orbit determination, calculation of covariance realism test statistics at each covariance propagation point, and proper assessment of those test statistics.
A-Train↗