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Small-Sample Estimator Decisions – Certainly Uncertain in Human Spaceflight at NASA

Within statistics when estimating means, we rely heavily on the Central Limit Theorem (CLT) to aid in our inference, however in cases where the CLT does not apply we begin to be strongly limited in our choices. If a violation to the CLT comes in the form of small samples and unknown population variance, yet we maintain the assumption of normality, the use of t-distributions is perfectly valid. We explore cases where population normality is not assumed, where sample sizes are small, and where some actionable estimate of the central tendency of a distribution is needed such as for spaceflight operational decisions. Here we identify different scenarios based on measures taken from spaceflight, characterizing performance of estimators of central tendency within our set of simulations. We examine bias and variability of standard estimators of central tendency as they apply to varying small sample sizes and varying population distributions. Further work in this area is needed to develop a framework or set of guidelines for individuals set in these situations. Even with limited information, decisions need to be made.

Central Tendency↗

NASA NTRS2019

Exploiting OMI NO2 Satellite Observations to Infer Fossil-fuel CO2 Emissions from U.S. Megacities

Fossil-fuel CO2 emissions and their trends in eight U.S. megacities during 2006–2017 are inferred by combining satellite-derived NOX emissions with bottom-up city-specific NOX-to-CO2 emission ratios. A statistical model is fit to a collection NO2 plumes observed from the Ozone Monitoring Instrument (OMI), and is used to calculate top-down NOX emissions. Decreases in OMI-derived NOX emissions are observed across the eight cities from 2006 to 2017 (−17% in Miami to −58% in Los Angeles), and are generally consistent with long-term trends of bottom-up inventories (−25% in Miami to −49% in Los Angeles), but there are some interannual discrepancies. City-specific NOX-to-CO2 emission ratios, used to calculate inferred CO2, are estimated through annual bottom-up inventories of NOX and CO2 emissions disaggregated to 1 × 1 km2 resolution. Over the study period, NOX-to-CO2 emission ratios have decreased by ~40% nationwide (−24% to −51% for our studied cities), which is attributed to a faster reduction in NOX when compared to CO2 due to policy regulations and fuel type shifts. Combining top-down NOX emissions and bottom-up NOX-to-CO2 emission ratios, annual fossil-fuel CO2 emissions are derived. Inferred OMI-based top-down CO2 emissions trends vary between +7% in Dallas to −31% in Phoenix. For 2017, we report annual fossil-fuel CO2 emissions to be: Los Angeles 113 ± 49 Tg/yr; New York City 144 ± 62 Tg/yr; and Chicago 55 ± 24 Tg/yr. A study in the Los Angeles area, using independent methods, reported a 2013–2016 average CO2 emissions rate of 104 Tg/yr and 120 Tg/yr, which suggests that the CO2 emissions from our method are in good agreement with other studies' top-down estimates. We anticipate future remote sensing instruments – with better spatial and temporal resolution – will better constrain the NOX-to-CO2 ratio and reduce the uncertainty in our method.

Ozone Monitoring Instrument (OMI)↗

NASA NTRS2017

Network Analysis of Rodent Transcriptomes in Spaceflight

Network analysis methods leverage prior knowledge of cellular systems and the statistical and conceptual relationships between analyte measurements to determine gene connectivity. Correlation and conditional metrics are used to infer a network topology and provide a systems-level context for cellular responses. Integration across multiple experimental conditions and omics domains can reveal the regulatory mechanisms that underlie gene expression. GeneLab has assembled rich multi-omic (transcriptomics, proteomics, epigenomics, and epitranscriptomics) datasets for multiple murine tissues from the Rodent Research 1 (RR-1) experiment. RR-1 assesses the impact of 37 days of spaceflight on gene expression across a variety of tissue types, such as adrenal glands, quadriceps, gastrocnemius, tibalius anterior, extensor digitorum longus, soleus, eye, and kidney. Network analysis is particularly useful for RR-1 -omics datasets because it reinforces subtle relationships that may be overlooked in isolated analyses and subdues confounding factors. Our objective is to use network analysis to determine potential target nodes for therapeutic intervention and identify similarities with existing disease models. Multiple network algorithms are used for a higher confidence consensus.

genomics↗

NASA NTRS1976

Nondeterministic data base for computerized visual perception

A description is given of the knowledge representation data base in the perception subsystem of the Mars robot vehicle prototype. Two types of information are stored. The first is generic information that represents general rules that are conformed to by structures in the expected environments. The second kind of information is a specific description of a structure, i.e., the properties and relations of objects in the specific case being analyzed. The generic knowledge is represented so that it can be applied to extract and infer the description of specific structures. The generic model of the rules is substantially a Bayesian representation of the statistics of the environment, which means it is geared to representation of nondeterministic rules relating properties of, and relations between, objects. The description of a specific structure is also nondeterministic in the sense that all properties and relations may take a range of values with an associated probability distribution.

Yakimovsky, Y.↗

NASA NTRS1984

Crop moisture estimation over the southern Great Plains with dual polarization 1.66 centimeter passive microwave data from Nimbus 7

Moisture content of snow-free, unfrozen soil is inferred using passive microwave brightness temperatures from the scanning multichannel microwave radiometer (SMMR) on Nimbus-7. Investigation is restricted to the two polarizations of the 1.66 cm wavelength sensor. Passive microwave estimates of soil moisture are of two basic categories; those based upon soil emissivity and those based upon the polarization of soil emission. The two methods are compared and contrasted through the investigation of 54 potential functions of polarized brightness temperatures and, in some cases, ground-based temperature measurements. Of these indices, three are selected for the estimated emissivity, the difference between polarized brightness temperatures, and the normalized polarization difference. Each of these indices is about equally effective for monitoring soil moisture. Using an antecedent precipitation index (API) as ground control data, temporal and spatial analyses show that emissivity data consistently give slightly better soil moisture estimates than depolarization data. The difference, however, is not statistically significant. It is concluded that polarization data alone can provide estimates of soil moisture in areas where the emissivity cannot be inferred due to nonavailability of surface temperature data.

Mcfarland, M. J.↗

NASA NTRS2013

Spatial Statistical Data Fusion (SSDF)

As remote sensing for scientific purposes has transitioned from an experimental technology to an operational one, the selection of instruments has become more coordinated, so that the scientific community can exploit complementary measurements. However, tech nological and scientific heterogeneity across devices means that the statistical characteristics of the data they collect are different. The challenge addressed here is how to combine heterogeneous remote sensing data sets in a way that yields optimal statistical estimates of the underlying geophysical field, and provides rigorous uncertainty measures for those estimates. Different remote sensing data sets may have different spatial resolutions, different measurement error biases and variances, and other disparate characteristics. A state-of-the-art spatial statistical model was used to relate the true, but not directly observed, geophysical field to noisy, spatial aggregates observed by remote sensing instruments. The spatial covariances of the true field and the covariances of the true field with the observations were modeled. The observations are spatial averages of the true field values, over pixels, with different measurement noise superimposed. A kriging framework is used to infer optimal (minimum mean squared error and unbiased) estimates of the true field at point locations from pixel-level, noisy observations. A key feature of the spatial statistical model is the spatial mixed effects model that underlies it. The approach models the spatial covariance function of the underlying field using linear combinations of basis functions of fixed size. Approaches based on kriging require the inversion of very large spatial covariance matrices, and this is usually done by making simplifying assumptions about spatial covariance structure that simply do not hold for geophysical variables. In contrast, this method does not require these assumptions, and is also computationally much faster. This method is fundamentally different than other approaches to data fusion for remote sensing data because it is inferential rather than merely descriptive. All approaches combine data in a way that minimizes some specified loss function. Most of these are more or less ad hoc criteria based on what looks good to the eye, or some criteria that relate only to the data at hand.

Braverman, Amy J.↗

NASA NTRS2009

Statistical and Scaling Properties of Remotely-Sensed Soil Moisture in Two Contrasting Domains in the North American Monsoon Region

Characterizing soil moisture (theta) variability is important for inferring high-resolution information from coarse estimates provided by remote sensors. In this study, we analyze the spatial variability and scale invariance of high-resolution theta estimates collected in two contrasting semiarid areas, Arizona (AZ) and Sonora (SON), during the Soil Moisture Experiment - North American Monsoon in 2004 (SMEX04- NAME). Results reveal that as the mean theta condition ( ) becomes drier, the spatial standard deviation becomes smaller in both domains. The coefficient of variation of theta decreases with in SON, but does not display a clear tendency with in AZ. We also found the presence of scale invariance and multifractality in the range of support scales from 51.2 km to 0.8 km for all soil moisture fields in the two regions. The multifractal properties of theta are clearly linked to in SON, while the relation is affected by more dispersion in AZ. We argue this is due to differences in the dynamic (rainfall) and static (vegetation) controls on theta in the two domains.

Mascaro, Giuseppe↗

NASA NTRS1990

Tensile adhesion testing methodology for thermally sprayed coatings

The structure of thermally sprayed coatings consists of lamellae which are oriented parallel to the substrate surface. The lamellae separate and fracture by distinctive mechanisms which are reflected in the failure morphology, and these may be described as adhesive (between the coating and substrate), cohesive (within the coating), or mixed mode. There is a large variability in the failure stress for any nominally identical group of coatings. A lower bound for the fracture toughness of alumina coatings can be calculated as 0.2 MNm exp -3/2. The coating strength values may also be treated as belonging to the statistical distribution of the Weibull function. The Weibull modulus of the coating strength varied from 1.4 to 3.8. This analysis infers that the flaw size within coatings is highly variable and that the flaws are nonuniformly dispersed. The present work focuses on the question of whether tensile adhesion tests are an appropriate testing method for thermally sprayed materials.

Berndt, Christopher C.↗

NASA NTRS1993

Comparative study of x ray and microwave emissions during solar flares

The work supported by the grant consisted of two projects. The first project involved making detailed case studies of two flares using SMM data in conjunction with ground based observations. The first flare occurred at 1454 UT on June 20, 1989 and involved the eruption of a prominence near the limb. In the study we used data from many wavelength regimes including the radio, H-alpha, hard X-rays, and soft X-rays. We used a full gyrosynchrotron code to model the apparent presence of a 1.4 GHz source early in the flare that was in the form of a large coronal loop. The model results lead us to conclude that the initial acceleration occurs in small, dense loops which also produced the flare's hard X-ray emission. We also found evidence that a source at 1.4 GHz later in the event was due to second harmonic plasma emission. This source was adjacent to a leg of the prominence and comes from a dense column of material in the magnetic structure supporting the prominence. Finally, we investigated a source of microwaves and soft X-rays, occurring approximately 10 min after the hard X-ray peak, and calculate a lower limit for the density of the source. The second flare that was studied occurred at 2156 UT on June 20, 1989 and was observed with the VLA and the Owens Valley Radio Observatory (OVRO) Frequency Agile Array. We have developed a gyrosynchrotron model of the sources at flare peak using a new gyrosynchrotron approximation which is valid at very low harmonics of the gyrofrequency. We found that the accelerated particle densities of the sources decreased much more with radius from the source center than had been supposed in previous work, while the magnetic field varied less. We also used the available data to analyze a highly polarized source which appeared late in the flare. The second project involved compiling a statistical base for the relative timing of the hard X-ray peak, the turbulent and blue-shift velocities inferred from soft X-ray line emissions observed by SMM and the microwave peak as determined from ground-based observations. This timing was then used to aid the testing of newly developed global models for flares that incorporate the global magnetic topology as well as the electron dynamics that are responsible for the hard X-rays and microwaves.

Winglee, Robert M.↗

NASA NTRS2018

MMS Examination of FTEs at the Earth's Subsolar Magnetopause

Determining the magnetic field structure, electric currents, and plasma distributions within flux transfer event (FTE)-type flux ropes is critical to the understanding of their origin, evolution, and dynamics. Here the Magnetospheric Multiscale mission's high-resolution magnetic field and plasma measurements are used to identify FTEs in the vicinity of the subsolar magnetopause. The constant-alpha flux rope model is used to identify quasi-force free flux ropes and to infer the size, the core magnetic field strength, the magnetic flux content, and the spacecraft trajectories through these structures. Our statistical analysis determines a mean diameter of 1,700 ± 400 km (~30 ± 9 d(sub i)) and an average magnetic flux content of 100 ± 30 kWb for the quasi-force free FTEs at the Earth's subsolar magnetopause which are smaller than values reported by Cluster at high latitudes. These observed nonlinear size and magnetic flux content distributions of FTEs appear consistent with the plasmoid instability theory, which relies on the merging of neighboring, small-scale FTEs to generate larger structures. The ratio of the perpendicular to parallel components of current density, R(sub J), indicates that our FTEs are magnetically force-free, defined as R(sub J) < 1, in their core regions (<0.6 R(sub flux rope)). Plasma density is shown to be larger in smaller, newly formed FTEs and dropping with increasing FTE size. It is also shown that parallel ion velocity dominates inside FTEs with largest plasma density. Field-aligned flow facilitates the evacuation of plasma inside newly formed FTEs, while their core magnetic field strengthens with increasing FTE size.

Akhavan-Tafti, M.↗

NASA NTRS2012

Inferred Lunar Boulder Distributions at Decimeter Scales

Block size distributions of impact deposits on the Moon are diagnostic of the impact process and environmental effects, such as target lithology and weathering. Block size distributions are also important factors in trafficability, habitability, and possibly the identification of indigenous resources. Lunar block sizes have been investigated for many years for many purposes [e.g., 1-3]. An unresolved issue is the extent to which lunar block size distributions can be extrapolated to scales smaller than limits of resolution of direct measurement. This would seem to be a straightforward statistical application, but it is complicated by two issues. First, the cumulative size frequency distribution of observable boulders rolls over due to resolution limitations at the small end. Second, statistical regression provides the best fit only around the centroid of the data [4]. Confidence and prediction limits splay away from the best fit at the endpoints resulting in inferences in the boulder density at the CPR scale that can differ by many orders of magnitude [4]. These issues were originally investigated by Cintala and McBride [2] using Surveyor data. The objective of this study was to determine whether the measured block size distributions from Lunar Reconnaissance Orbiter Camera - Narrow Angle Camera (LROC-NAC) images (m-scale resolution) can be used to infer the block size distribution at length scales comparable to Mini-RF Circular Polarization Ratio (CPR) scales, nominally taken as 10 cm. This would set the stage for assessing correlations of inferred block size distributions with CPR returns [6].

Baloga, S. M.↗

NASA NTRS1980

Inversion of multiwavelength radiometer measurements by three-dimensional filtering

Remote sensing data from satellites typically have three dimensions: scan position, spacecraft position, and wavelength. Inversion of the radiometric data to infer geophysical parameters is a filtering problem in which the dimension of wavelength (or channel number) is transformed into a dimension of geophysical parameters, and the most general solution is a three-dimensional filter. Linear filters have the advantages of computational speed and easily described transfer functions; but often the measurements are nonlinear functions of the parameters to be inferred. To the extent that the nonlinear inversion problem is overdetermined, it can be modeled by a critically determined linear problem. As an example, inversion of Scanning Multichannel Microwave Radiometer (SMMR) data by means of a three-dimensional Wiener Filter is described. Atmospheric water vapor content, rain liquid water content, surface wind speed and surface temperature are the parameters inferred from the measurements. Nonprecipitating liquid water and water vapor scale height are also modeled but not retrieved. The a priori statistics on which the filter is trained have the effect of governing the selection of a trade-off point of noise as a function of resolution (in all three retrieval dimensions).

Rosenkranz, P. W.↗

NASA NTRS1985

Observed relation between thermal emission and reflected spectral radiance of a complex vegetated landscape

An investigation is conducted, for a complex vegetated land area, into the statistical relationship between remotely sensed thermal emissions and reflected spectral radiance. The Kauth-Thomas Tasseled Cap transformation is employed to infer the albedo and amount of green vegetation present from Landsat multispectral scanner (MSS) observations. Reflective data and thermal infrared data were acquired from the Heat Capacity Mapping Mission (HCMM) satellite along with reflective data from the Landsat 3 MSS for a site near Hartford, CT on a single date. Results are presented which indicate that thermal emissions had the greatest association with the amount of vegetation as indicated by a multispectral index, while albedo did not exhibit any substantial relationship with these emissions. These findings are explained in terms of the enhanced latent heat flux to the atmosphere associated with actively transpiring vegetation.

Goward, S. N.↗

NASA NTRS2017

Advances in Medical Analytics Solutions for Autonomous Medical Operations on Long-Duration Missions

A review will be presented on the progress made under STMDGame Changing Development Program Funding towards the development of a Medical Decision Support System for augmenting crew capabilities during long-duration missions, such as Mars Transit. To create an MDSS, initial work requires acquiring images and developing models that analyze and assess the features in such medical biosensor images that support medical assessment of pathologies. For FY17, the project has focused on ultrasound images towards cardiac pathologies: namely, evaluation and assessment of pericardial effusion identification and discrimination from related pneumothorax and even bladder-induced infections that cause inflammation around the heart. This identification is substantially changed due to uncertainty due to conditions of fluid behavior under space-microgravity. This talk will present and discuss the work-to-date in this Project, recognizing conditions under which various machine learning technologies, deep-learning via convolutional neural nets, and statistical learning methods for feature identification and classification can be employed and conditioned to graphical format in preparation for attachment to an inference engine that eventually creates decision support recommendations to remote crew in a triage setting.

Medical Decision Support Systems↗

NASA NTRS2018

Flood Hazard Assessment from Storm Tides, Rain and Sea Level Rise for a Tidal River Estuary

Cities and towns along the tidal Hudson River are highly vulnerable to flooding through the combination of storm tides and high streamflows, compounded by sea level rise. Here a three-dimensional hydrodynamic model, validated by comparing peak water levels for 76 historical storms, is applied in a probabilistic flood hazard assessment. In simulations, the model merges streamflows and storm tides from tropical cyclones (TCs), offshore extratropical cyclones (ETCs) and inland "wet extratropical" cyclones (WETCs). The climatology of possible ETC and WETC storm events is represented by historical events (1931-2013), and simulations include gauged streamflows and inferred ungauged streamflows (based on watershed area) for the Hudson River and its tributaries. The TC climatology is created using a stochastic statistical model to represent a wider range of storms than is contained in the historical record. TC streamflow hydrographs are simulated for tributaries spaced along the Hudson, modeled as a function of TC attributes (storm track, sea surface temperature, maximum wind speed) using a statistical Bayesian approach. Results show WETCs are important to flood risk in the upper tidal river (e.g., Albany, New York), ETCs are important in the estuary (e.g., New York City) and lower tidal river, and TCs are important at all locations due to their potential for both high surge and extreme rainfall. The raising of floods by sea level rise is shown to be reduced by approximately 30-60 percent at Albany due to the dominance of streamflow for flood risk. This can be explained with simple channel flow dynamics, in which increased depth throughout the river reduces frictional resistance, thereby reducing the water level slope and the upriver water level.

Tidal river↗

NASA NTRS1988

Confidence set inference with a prior quadratic bound

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.

Backus, George E.↗

NASA NTRS1992

Statistics of gamma-ray bursts - Homogeneous spherical models

Early reports from the BATSE experiment seem to suggest that the observed gamma-ray bursts occur in a highly flattened region of space. This inference, however, is contradicted by the apparent isotropy of the bursts. Here, it is demonstrated that this apparent dilemma can be resolved in a straightforward manner if bursts occur in a bounded spherical volume centered about the observer. Such a geometrical distribution of the bursts can be consistent with the apparent isotropy of the bursts. Two different models in which the burst population is uniformly distributed in a bounded spherical region of space are considered.

Wasserman, Ira↗

NASA NTRS2003

HARLIE Aerosol and Cloud Structure and Wind Observations during HARGLO and IHOP

The Holographic Airborne Rotating Lidar Instrument Experiment (HARLIE) is a conical-scanning, 1-micron wavelength lidar that has been adapted for ground-based applications and used to infer horizontal wind information by tracking the motions of aerosol and cloud scattering structures. In addition, HARLIE's rapid continuous scanning enables boundary layer statistics and a new cloud lidar data product that gives cloud coverage as a function of altitude with high temporal resolution. HARLIE has been used in several field campaigns while developing the techniques for wind, boundary layer (BL), and cloud data products. These campaigns involved a variety of wind measuring instruments including rawindsondes, cloud-tracked winds from video imagery, Doppler lidars and Doppler radars. HARGLO-2 was one of these campaigns and was dedicated to wind profile intercomparisons over a 1-week period in November of 2001. The most recent of these campaigns was the International H20 Project (IHOP) located in the Southern Great Plains of the US during May and June of 2002.

Schwemmer, Geary K.↗