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All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Comparison of Statistically Modeled Contaminated Soil Volume Estimates and Actual Excavation Volumes at the Maywood FUSRAP Site - 13555

As part of the ongoing remediation process at the Maywood Formerly Utilized Sites Remedial Action Program (FUSRAP) properties, Argonne National Laboratory (Argonne) assisted the U.S. Army Corps of Engineers (USACE) New York District by providing contaminated soil volume estimates for the main site area, much of which is fully or partially remediated. As part of the volume estimation process, an initial conceptual site model (ICSM) was prepared for the entire site that captured existing information (with the exception of soil sampling results) pertinent to the possible location of surface and subsurface contamination above cleanup requirements. This ICSM was based on historical anecdotal information, aerial photographs, and the logs from several hundred soil cores that identified the depth of fill material and the depth to bedrock under the site. Specialized geostatistical software developed by Argonne was used to update the ICSM with historical sampling results and down-hole gamma survey information for hundreds of soil core locations. The updating process yielded both a best guess estimate of contamination volumes and a conservative upper bound on the volume estimate that reflected the estimate's uncertainty. Comparison of model results to actual removed soil volumes was conducted on a parcel-by-parcel basis. Where sampling data density was adequate, the actual volume matched the model's average or best guess results. Where contamination was un-characterized and unknown to the model, the actual volume exceeded the model's conservative estimate. Factors affecting volume estimation were identified to assist in planning further excavations. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

A Provably Accurate Randomized Sampling Algorithm for Logistic Regression

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.

Chowdhury, Agniva↗
DOE OSTI2021

Nearly hyperuniform, nonhyperuniform, and antihyperuniform density fluctuations in two-dimensional transition metal dichalcogenides with defects

Hyperuniform many-body systems in d-dimensional Euclidean space R d are characterized by completely suppressed (normalized) infinite-wavelength density fluctuations, and appear to be endowed with novel exotic physical properties. Recently, hyperuniform systems of disordered varieties have been observed in the context of various atomic-scale two-dimensional (2D) materials. Here, we analyze the effects of localized defects on the density fluctuations across length scales and on the hyperuniformity property of experimental samples of two-dimensional transition metal dichalcogenides. In particular, we extract atomic coordinates from time series annular dark field-scanning transmission electron microscopy (ADF-STEM) imaging data of 2D tungsten chalcogenides with the 2H structure (Te-doped 2H-WSe 2 ) showing continuous development and evolution of electron-beam induced defects, and construct the corresponding chemical-bonding informed coordination networks between the atoms. We then compute a variety of pair statistics and bond-orientational statistics to characterize the samples. At low defect concentrations, the corresponding materials are nearly hyperuniform, characterized by significantly suppressed scattering at the zero wave-number limit (omitting forward/ballistic scattering). As more defects are introduced, the (approximate) hyperuniformity of the materials is gradually destroyed, and the system becomes non-hyperuniform even when the material still contains a significant amount of crystalline regions. At high defect concentrations, the structures become antihyperuniform with diverging (normalized) large-scale density fluctuations, mimicking those typically observed at the thermal critical points associated with phase transitions. Overall, the defected materials possess varying degrees of orientation order, and there is apparently no intermediate hexatic phase emerging. To understand the observed nearly hyperuniform density fluctuations in the slightly defected materials, we construct a minimalist structural model and demonstrate that the experimental samples can be essentially viewed as perturbed honeycomb crystals with small correlated displacements and double chalcogen vacancies. Moreover, the small correlated displacements alone can significantly degrade hyperuniformity of the perfect honeycomb structure. Therefore, even a small amount of vacancies, when coupled with correlated displacements, can completely destroy hyperuniformity of the system.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2015

Sanov and central limit theorems for output statistics of quantum Markov chains

In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Such higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2002

Investigation of Error Patterns in Geographical Databases

The objective of the research conducted in this project is to develop a methodology to investigate the accuracy of Airport Safety Modeling Data (ASMD) using statistical, visualization, and Artificial Neural Network (ANN) techniques. Such a methodology can contribute to answering the following research questions: Over a representative sampling of ASMD databases, can statistical error analysis techniques be accurately learned and replicated by ANN modeling techniques? This representative ASMD sample should include numerous airports and a variety of terrain characterizations. Is it possible to identify and automate the recognition of patterns of error related to geographical features? Do such patterns of error relate to specific geographical features, such as elevation or terrain slope? Is it possible to combine the errors in small regions into an error prediction for a larger region? What are the data density reduction implications of this work? ASMD may be used as the source of terrain data for a synthetic visual system to be used in the cockpit of aircraft when visual reference to ground features is not possible during conditions of marginal weather or reduced visibility. In this research, United States Geologic Survey (USGS) digital elevation model (DEM) data has been selected as the benchmark. Artificial Neural Networks (ANNS) have been used and tested as alternate methods in place of the statistical methods in similar problems. They often perform better in pattern recognition, prediction and classification and categorization problems. Many studies show that when the data is complex and noisy, the accuracy of ANN models is generally higher than those of comparable traditional methods.

Dryer, David↗
DOE OSTI2011

Statistical variability and confidence intervals for planar dose QA pass rates

Purpose: The most common metric for comparing measured to calculated dose, such as for pretreatment quality assurance of intensity-modulated photon fields, is a pass rate (%) generated using percent difference (%Diff), distance-to-agreement (DTA), or some combination of the two (e.g., gamma evaluation). For many dosimeters, the grid of analyzed points corresponds to an array with a low areal density of point detectors. In these cases, the pass rates for any given comparison criteria are not absolute but exhibit statistical variability that is a function, in part, on the detector sampling geometry. In this work, the authors analyze the statistics of various methods commonly used to calculate pass rates and propose methods for establishing confidence intervals for pass rates obtained with low-density arrays. Methods: Dose planes were acquired for 25 prostate and 79 head and neck intensity-modulated fields via diode array and electronic portal imaging device (EPID), and matching calculated dose planes were created via a commercial treatment planning system. Pass rates for each dose plane pair (both centered to the beam central axis) were calculated with several common comparison methods: %Diff/DTA composite analysis and gamma evaluation, using absolute dose comparison with both local and global normalization. Specialized software was designed to selectively sample the measured EPID response (very high data density) down to discrete points to simulate low-density measurements. The software was used to realign the simulated detector grid at many simulated positions with respect to the beam central axis, thereby altering the low-density sampled grid. Simulations were repeated with 100 positional iterations using a 1 detector/cm{sup 2} uniform grid, a 2 detector/cm{sup 2} uniform grid, and similar random detector grids. For each simulation, %/DTA composite pass rates were calculated with various %Diff/DTA criteria and for both local and global %Diff normalization techniques. Results: For the prostate and head/neck cases studied, the pass rates obtained with gamma analysis of high density dose planes were 2%-5% higher than respective %/DTA composite analysis on average (ranging as high as 11%), depending on tolerances and normalization. Meanwhile, the pass rates obtained via local normalization were 2%-12% lower than with global maximum normalization on average (ranging as high as 27%), depending on tolerances and calculation method. Repositioning of simulated low-density sampled grids leads to a distribution of possible pass rates for each measured/calculated dose plane pair. These distributions can be predicted using a binomial distribution in order to establish confidence intervals that depend largely on the sampling density and the observed pass rate (i.e., the degree of difference between measured and calculated dose). These results can be extended to apply to 3D arrays of detectors, as well. Conclusions: Dose plane QA analysis can be greatly affected by choice of calculation metric and user-defined parameters, and so all pass rates should be reported with a complete description of calculation method. Pass rates for low-density arrays are subject to statistical uncertainty (vs. the high-density pass rate), but these sampling errors can be modeled using statistical confidence intervals derived from the sampled pass rate and detector density. Thus, pass rates for low-density array measurements should be accompanied by a confidence interval indicating the uncertainty of each pass rate.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2023

DESI and DECaLS (D&D): galaxy–galaxy lensing measurements with 1 per cent survey and its forecast

The shear measurement from the Dark Energy Camera Legacy Survey (DECaLS) provides an excellent opportunity for galaxy–galaxy lensing study with the Dark Energy Spectroscopic Instrument (DESI) galaxies, given the large (~9000 deg 2 ) sky overlap. We explore this potential by combining the DESI 1 per cent survey and DECaLS Data Release 8 (DR8). With ~106 deg 2 sky overlap, we achieve significant detection of galaxy–galaxy lensing for Bright Galaxy Survey (BGS) and luminous red galaxy (LRG) as lenses. Scaled to the full BGS sample, we expect the statistical errors to improve from 18(12)per cent to a promising level of 2(1.3)per cent at θ > 8arcmin(< 8 arcmin) ⁠. This brings stronger requirements for future systematics control. To fully realize such potential, we need to control the residual multiplicative shear bias |m| < 0.006 and the bias in the mean redshift |Δz| < 0.008, requiring the introduced bias in the measurement is <0.31σ. We also expect significant detection of galaxy–galaxy lensing with DESI LRG/emission line galaxy (ELG) full samples as lenses, and cosmic magnification of ELG through cross-correlation with low-redshift DECaLS shear. If such systematical error control can be achieved, we find the advantages of DECaLS, comparing with the Kilo Degree Survey (KiDS) and the Hyper Suprime-Cam (HSC), are at low redshift, large scale, and in measuring the shear ratio (to σ R ~ 0.04) and cosmic magnification.

(cosmology:) large-scale structure of Universe↗
DOE OSTI2012

AN UPDATED CATALOG OF M33 CLUSTERS AND CANDIDATES: UBVRI PHOTOMETRY AND SOME STATISTICAL RESULTS

We present UBVRI photometry for 392 star clusters and candidates in the field of M33, which are selected from the most recent star cluster catalog. In this catalog, the authors listed star clusters' parameters such as cluster positions, magnitudes, colors in the UBVRIJHK{sub s} filters, and so on. However, a large fraction of objects in this catalog do not have previously published photometry. Photometry is performed using archival images from the Local Group Galaxies Survey, which covers 0.8 deg{sup 2} along the major axis of M33. Detailed comparisons show that, in general, our photometry is consistent with previous measurements. Positions (right ascension and declination) for some clusters are corrected here. Combined with previous literature, ours constitute a large sample of M33 star clusters. Based on this cluster sample, we present some statistical results: none of the youngest M33 clusters ({approx}10{sup 7} yr) have masses approaching 10{sup 5} M{sub Sun} ; roughly half the star clusters are consistent with the 10{sup 4}-10{sup 5} M{sub Sun} mass models; the continuous distribution of star clusters along the model line indicates that M33 star clusters have been formed continuously from the epoch of the first star cluster formation until recent times; and there are {approx}50 star clusters which are overlapped with the Galactic globular clusters on the color-color diagram, and these clusters are old globular cluster candidates in M33.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

The black hole mass function derived from local spiral galaxies

We present our determination of the nuclear supermassive black hole (SMBH) mass function for spiral galaxies in the local universe, established from a volume-limited sample consisting of a statistically complete collection of the brightest spiral galaxies in the southern (δ < 0°) hemisphere. Our SMBH mass function agrees well at the high-mass end with previous values given in the literature. At the low-mass end, inconsistencies exist in previous works that still need to be resolved, but our work is more in line with expectations based on modeling of black hole evolution. This low-mass end of the spectrum is critical to our understanding of the mass function and evolution of black holes since the epoch of maximum quasar activity. The sample is defined by a limiting luminosity (redshift-independent) distance, D{sub L} = 25.4 Mpc (z = 0.00572) and a limiting absolute B-band magnitude, M{sub B}=−19.12. These limits define a sample of 140 spiral galaxies, with 128 measurable pitch angles to establish the pitch angle distribution for this sample. This pitch-angle distribution function may be useful in the study of the morphology of late-type galaxies. We then use an established relationship between the logarithmic spiral arm pitch angle and the mass of the central SMBH in a host galaxy in order to estimate the mass of the 128 respective SMBHs in this volume-limited sample. This result effectively gives us the distribution of mass for SMBHs residing in spiral galaxies over a lookback time, t{sub L} ≤ 82.1 h{sub 67.77}{sup −1} Myr and contained within a comoving volume, V{sub C} = 3.37 × 10{sup 4} h{sub 67.77}{sup −3} Mpc{sup 3}. We estimate that the density of SMBHs residing in spiral galaxies in the local universe is ρ=5.54{sub −2.73}{sup +6.55} × 10{sup 4} h{sub 67.77}{sup 3} M{sub ☉} Mpc{sup –3}. Thus, our derived cosmological SMBH mass density for spiral galaxies is Ω{sub BH}=4.35{sub −2.15}{sup +5.14} × 10{sup –7} h{sub 67.77}. Assuming that black holes grow via baryonic accretion, we predict that 0.0020{sub −0.0010}{sup +0.0023} h{sub 67.77}{sup 3} % of the universal baryonic inventory (Ω{sub BH}/ω{sub b}) is confined within nuclear SMBHs at the center of spiral galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

The Impact of Below Detection Limit Samples in (NPP) Decommissioning Residual Risk Assessment - 17033

There are some technical problems with finalizing regulations and standards that address nuclear power plant (NPP) decommissioning site soil analyses for license termination. It is difficult to know how to best include detection limit observations from site soil analysis, because typical soil collection data is reported above, at, and below the detection limit. In addition, multiple detection limits are required to adequately estimate the soil radionuclide concentrations. In the literature, researchers analyzing environmental data refer to below the detection limit observations as 'left-censored data'. Left-censored data are less than the detection limit of the instrument(s) that made the measurements. Conventional approaches to managing left-censored data either ignore or simply replace the detection limits with zero, a fraction of the detection limit, or the detection limit itself. However, these approaches are statistically biased and limited in their usefulness. The Kaplan-Meier method, robust regression on order statistics method, and maximum likelihood estimation method are proposed to estimate the left-censored data more precisely. The proposed methods are applied to data from a Monazite powder manufacturing plant and the Colorado School of Mines Research Institute. Summary statistics such as the sample mean, sample standard deviation, sample percentiles are calculated from each data set and are used in risk and volume estimation calculations. Previous environmental analyses, such as the exposure assessment, recognize the uncertainty issue that is addressed in this research using the Latin hypercube sampling approach. Next, probabilistic distributions of the input parameters are developed for the uncertainty analyses. Finally, a framework methodology depicting the decision-making process in the proposed method is presented. The framework defines the critical steps, the amount of radioactivity, types of distributions, censoring percentage, sample size, and number of detection limits; it also allows the user to select the appropriate approach based on their site-specific data and analyses. The goal of this research is to develop a more precise risk assessment, estimate of the volume of soil removal, examine potential cost savings. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Advanced Models for Nondestructive Evaluation of Aging Nuclear Power Plant Cables

Background: Nuclear power plant (NPP) cables must function correctly for proper power supply and control of the nuclear reactor. This is especially important for public and environmental safety at critical times such as during reactor shut-down following loss of coolant. Over extended periods of service, the cable insulation and jacket polymer materials suffer from degradation due to exposure to environmental stressors such as heat and ionizing radiation. The focus of this project has been the development of detailed descriptions of the way in which insulation polymers degrade, from a materials science perspective, and the development of new electrical techniques to monitor cable polymer condition nondestructively. Objectives: The objectives of this project have been to i) perform detailed characterization experiments upon cable insulation polymers that have experienced thermal and radiation exposure mimicking that received during NPP operation, including the exploration of novel cable nondestructive evaluation methods; capacitive, THz and infrared methods; ii) identify the most sensitive indicators of aging in these materials, and iii) develop advanced, validated models describing microstructural and chemical changes that are observed in cable insulation polymers due to thermal and radiation exposure. Methods: Accelerated aging was performed on the two most common United States NPP cable insulation polymers (cross-linked polyethylene (XLPE) and ethylene propylene rubber (EPR)) under various conditions of elevated temperature and gamma radiation dose. Aging mechanisms were elucidated through extensive thermal, mechanical and microscopic characterization of the aged samples, and materials modeling. Dielectric and IR spectra were measured on pristine and aged samples. Data was analyzed statistically, via multiple linear regression, partial least squares and probabilistic neural network approaches. Impact: Extant cable monitoring techniques do not deal successfully with all polymer types. This research has laid a foundation upon which new electrical nondestructive test methods for cable polymer condition monitoring may be developed, hence launching the development of new test methods for cable insulation monitoring based on measuring electrical rather than mechanical parameters. Collaboration: This project has benefitted from collaboration between experts in materials science and engineering, materials modeling, electrical engineering, and nondestructive evaluation. The majority of the characterization measurements were carried out at Iowa State University. Materials modeling was carried out primarily at Washington State University. Irradiation of samples took place at Pacific Northwest National Laboratory (PNNL), where a student intern from Iowa State was hosted for one summer, setting up the aging experiments. A research student from the University of Bologna, Italy, joined the project for their thesis research at Iowa State University with samples provided by PNNL. The project benefitted from regular involvement of senior engineers in US-based industry partners. Project investigators presented findings at various national and international conferences and workshops.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1964

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↗
NASA NTRS1990

Analysis of sequencing and scheduling methods for arrival traffic

The air traffic control subsystem that performs scheduling is discussed. The function of the scheduling algorithms is to plan automatically the most efficient landing order and to assign optimally spaced landing times to all arrivals. Several important scheduling algorithms are described and the statistical performance of the scheduling algorithms is examined. Scheduling brings order to an arrival sequence for aircraft. First-come-first-served scheduling (FCFS) establishes a fair order, based on estimated times of arrival, and determines proper separations. Because of the randomness of the traffic, gaps will remain in the scheduled sequence of aircraft. These gaps are filled, or partially filled, by time-advancing the leading aircraft after a gap while still preserving the FCFS order. Tightly scheduled groups of aircraft remain with a mix of heavy and large aircraft. Separation requirements differ for different types of aircraft trailing each other. Advantage is taken of this fact through mild reordering of the traffic, thus shortening the groups and reducing average delays. Actual delays for different samples with the same statistical parameters vary widely, especially for heavy traffic.

Neuman, Frank↗
DOE OSTI2026

The DESI DR1 Peculiar Velocity Survey: Global Zero-point and H 0 Constraints

The Dark Energy Spectroscopic Instrument (DESI) in its first Data Release (DR1) already provides more than 100,000 galaxies with relative distance measurements. The primary purpose of this paper is to perform the calibration of the zero-point for the DESI Fundamental Plane and Tully–Fisher relations, which allows us to measure the Hubble constant, H 0 . This sample has a lower statistical uncertainty than any previously used to measure H 0 , and we investigate the systematic uncertainties in absolute calibration that could limit the accuracy of that measurement. We improve upon the DESI Early Data Release Fundamental Plane H 0 measurement by (a) using a group catalog to increase the number of calibrator galaxies and (b) investigating alternative calibrators in the nearby Universe. Our baseline measurement calibrates to the SH0ES/Pantheon+ type Ia supernovae, and finds H 0 = 73.7 ± 0.06 (stat.) ± 1.1 (syst.) km s −1 Mpc −1 . Calibrating to surface brightness fluctuation distances yields a similar H 0 . We explore measurements using other calibrators, but these are currently less precise since the overlap with DESI peculiar velocity tracers is much smaller. In future data releases with an even larger peculiar velocity sample, we plan to calibrate directly to Cepheids and the tip of the red giant branch, which will enable the uncertainty to decrease towards a percent-level measurement of H 0 . This will provide an alternative to supernovae as the Hubble flow sample for H 0 measurements.

Carr, Anthony [Korea Astronomy and Space Science I↗
DOE OSTI2016

Angular correlation between IceCube high-energy starting events and starburst sources

Starburst galaxies and star-forming regions in the Milkyway, with high rate of supernova activities, are candidate sources of high-energy neutrinos. Using a gamma-ray selected sample of these sources we perform statistical analysis of their angular correlation with the four-year sample of high-energy starting events (HESE), detected by the IceCube Neutrino Observatory. We find that the two samples (starburst galaxies and local star-forming regions) are correlated with cosmic neutrinos at ∼ (2–3)σ (pre-trial) significance level, when the full HESE sample with deposited energy ∼> 20 TeV is considered. However when we consider the HESE sample with deposited energy ∼> 60 TeV, which is almost free of atmospheric neutrino and muon backgrounds, the significance of correlation decreased drastically. We perform a similar study for Galactic sources in the 2nd Catalog of Hard Fermi -LAT Sources (2FHL, >50 GeV) catalog as well, obtaining ∼ (2–3)σ (pre-trial) correlation, however the significance of correlation increases with higher cutoff energy in the HESE sample for this case. We also fit available gamma-ray data from these sources using a pp interaction model and calculate expected neutrino fluxes. We find that the expected neutrino fluxes for most of the sources are at least an order of magnitude lower than the fluxes required to produce the HESE neutrinos from these sources. This puts the starburst sources being the origin of the IceCube HESE neutrinos in question.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Contributions of Various Radiological Sources to Background in a Suburban Environment

This work is a brief overview and comparison of dose rates stemming from both indoor and outdoor natural background radiation and household objects within a suburban environment in North Carolina. Combined gamma and beta dose rates were taken from indoor objects that ranged from the potassium in fruit to the americium in smoke detectors. For outdoor measurements, various height and time data samples were collected to show fluctuations in dose rate due to temperature inversion and geometric attenuation. Although each sample tested proved to have a statistically significant increase over background using Students t-test, no sample proved to be more than a minor increase in natural radiation dose. Furthermore, the relative contributions from natural radioactivity such as potassium in foods and common household items are shown to be easily distinguished from background using standard handheld instrumentation when applied in a systematic, methodological manner.

61 RADIATION PROTECTION AND DOSIMETRY↗
NASA NTRS2006

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.↗