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At least 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted

Pohorille, Andrew↗
DOE OSTI2021

Equilibrium distribution of point defects in Fe-Y-O as a typical representative of nanocluster-strengthened alloys

The statistical mechanic approach has been used to estimate the equilibrium defect distribution in a multiphase system by minimizing its free energy using microstructural characteristics and a finite set of defects obtained by first-principles calculations. Recently the approach was extended to take in consideration defects at the interface of the precipitate and matrix. Herein we apply the developed approach to the investigation of the stability of bcc Fe containing yttria, Y 2 O 3 , nanoclusters as a prototype of nanostructured ferritic alloys. It has been obtained that (100)Fe-O interface is unstable with respect to vacancies production. In a contrast to (100)Fe-O interface, the so called Klim interface is stable, i.e. local vacancy concentration at this interface at 600 K is below 10 -12 . It has been demonstrated that due to large defect formation energies the ODS particles are extremely stable and the main defect corresponds to Fe atoms substitute Y in Y 2 O 3 precipitate. Moreover, under thermodynamic equilibrium condition, the preexist vacancies in bulk Fe do not accumulate oxygen atom. The later observation not necessarily forbid the existence of a large amount of preexisting Fe vacancy - oxygen atom clusters at the initial stages of alloy formation far from equilibrium.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Widths of transverse momentum distributions in intermediate-energy heavy-ion collisions

The need to include dynamical collision momentum transfer contributions, arising from interacting nuclear and Coulomb fields, to estimates of fragment momentum distributions is discussed. Methods based upon an optical potential model are presented. Comparisons with recent experimental data of the Siegen group for variances of transverse momentum distributions for gold nuclei at 980 A MeV fragmenting on silver foil and plastic nuclear track detector targets are made. The agreement between theory and experiment is good.

Khan, Ferdous↗
NASA NTRS1988

The identification of a distributed parameter model for a flexible structure

A computational method is developed for the estimation of parameters in a distributed model for a flexible structure. The structure we consider (part of the RPL experiment) consists of a cantilevered beam with a thruster and linear accelerometer at the free end. The thruster is fed by a pressurized hose whose horizontal motion effects the transverse vibration of the beam. The Euler-Bernoulli theory is used to model the vibration of the beam and treat the hose thruster assembly as a lumped or point mass dashpot spring system at the tip. Measurements of linear acceleration at the tip are used to estimate the hose parameters (mass, stiffness, damping) and a Voigt-Kelvin viscoelastic structural damping parameter for the beam using a least squares fit to the data. Spline based approximations are considered to the hybrid (coupled ordinary and partial differential equations) systems; theoretical convergence results and numerical studies with both simulation and actual experimental data obtained from the structure are presented and discussed.

Banks, H. T.↗
NASA NTRS1986

The identification of a distributed parameter model for a flexible structure

A computational method is developed for the estimation of parameters in a distributed model for a flexible structure. The structure we consider (part of the RPL experiment) consists of a cantilevered beam with a thruster and linear accelerometer at the free end. The thruster is fed by a pressurized hose whose horizontal motion effects the transverse vibration of the beam. The Euler-Bernoulli theory is used to model the vibration of the beam and treat the hose-thruster assembly as a lumped or point mass-dashpot-spring system at the tip. Using measurements of linear acceleration at the tip, it is estimated that the parameters (mass, stiffness, damping) and a Voight-Kelvin viscoelastic structural damping parameter for the beam using a least squares fit to the data. Spline based approximations to the hybrid (coupled ordinary and partial differential equations) system are considered; theoretical convergence results and numerical studies with both simulation and actual experimental data obtained from the structure are presented and discussed.

Banks, H. T.↗
NASA NTRS1995

Application of Image Analysis for Characterization of Spatial Arrangements of Features in Microstructure

A number of microstructural processes are sensitive to the spatial arrangements of features in microstructure. However, very little attention has been given in the past to the experimental measurements of the descriptors of microstructural distance distributions due to the lack of practically feasible methods. We present a digital image analysis procedure to estimate the micro-structural distance distributions. The application of the technique is demonstrated via estimation of K function, radial distribution function, and nearest-neighbor distribution function of hollow spherical carbon particulates in a polymer matrix composite, observed in a metallographic section.

Louis, Pascal↗
NASA NTRS2002

Evaluation of Improvements to the TRMM Microwave Rain Algorithm

Improvements made to the Version 5 TRMM passive microwave rain retrieval algorithm (2A-12) are evaluated using independent data. Surface rain rate estimates from the Version 5 TRMM TMI (2A-12), PR (2A-25) and TMI/PR Combined (2B-31) algorithms and ground-based radar estimates for selected coincident subset datasets in 1998 over Melbourne and Kwajalein show varying degrees of agreement. The surface rain rates are then classified into convective and stratiform rain types over ocean, land, and coastal areas for more detailed comparisons to the ground radar measurements. These comparisons lead to a better understanding of the relative performances of the current TRMM rain algorithms. For example, at Melbourne more than 80% of the radar-derived rainfall is classified as convective rain. Convective rain from the TRMM rain algorithms is less than that from ground radar measurements, while TRMM stratiform rain is much greater. Rain area coverage from 2A-12 is also in reasonable agreement with ground radar measurements, with about 25% more over ocean and 25% less over land and coastal areas. Retrieved rain rates from the improved (Version 6) 2A-12 algorithm will be compared to 2A-25, 2B-31, and ground-based radar measurements to evaluate the impact of improvements to 2A-12 in Version 6. An important improvement to the Version 6 2A-12 algorithm is the retrieval of Q1/Q2 (latent heating/drying) profiles in addition to the surface rain rate and hydrometeor profiles. In order to ascertain the credibility of the new products, retrieved Q1/Q2 profiles are compared to independent ground-based estimates. Analyses of dual-Doppler radar data in conjunction with coincident rawinsonde data yield estimates of the vertical distributions of diabatic heating/drying at high horizontal resolution for selected cases over the Kwajalein and LBA field sites. The estimated vertical heating/drying structures appear to be reasonable. Comparisons of Q1/Q2 profiles from Version 6 2A-12 and the ground-based estimates are in progress. Retrieved Q1/Q2 structures will also be compared to MM5 hurricane simulations for selected cases. The results of these intercomparisons will be presented at the conference.

Yang, Song↗
NASA NTRS2013

Evidence of a Weakly Absorbing Intermediate Mode of Aerosols in AERONET Data from Saharan and Sahelian Sites

Accurate retrievals of aerosol size distribution are necessary to estimate aerosols' impact on climate and human health. The inversions of the Aerosol Robotic Network (AERONET) usually retrieve bimodal distributions. However, when the inversion is applied to Saharan and Sahelian dust, an additional mode of intermediate size between the coarse and fine modes is sometimes seen. This mode explains peculiarities in the behavior of the Angstrom exponent, along with the fine mode fraction retrieved using the spectral deconvolution algorithm, observed in a March 2006 dust storm. For this study, 15 AERONET sites in northern Africa and on the Atlantic are examined to determine the frequency and properties of the intermediate mode. The mode is observed most frequently at Ilorin in Nigeria. It is also observed at Capo Verde and multiple sites located within the Sahel but much less frequently at sites in the northern Sahara and the Canary Islands. The presence of the intermediate mode coincides with increases in Angstrom exponent, fine mode fraction, single-scattering albedo, and to a lesser extent percent sphericity. The Angstrom exponent decreases with increasing optical depth at most sites when the intermediate mode is present, but the fine mode fraction does not. Single-scattering albedo does not steadily decrease with fine mode fraction when the intermediate mode is present, as it does in typical mixtures of dust and biomass-burning aerosols. Continued investigation is needed to further define the intermediate mode's properties, determine why it differs from most Saharan dust, and identify its climate and health effects.

inversions↗
NASA NTRS1990

Spatial variability of rain rate and slant path attenuation distributions at 28 GHz in the mid-Atlantic coast region of the United States

Rain rate and corresponding estimated slant-path attenuation distributions derived from two years of measurements are presented for a network of nine rain-gage sites located in a region with extent 70 km N-S and 47 km E-W in the mid-Atlantic coast of the U.S. near the NASA Wallops Flight Facility, VA. The network average rain-rate distribution was compared with a previously measured 6-year average at one of the site locations. Agreement in rain rates was found to be within approximately 1 mm/h over the percentage range of 1-0.01 percent of the year, signifying the constancy of the rain-rate climatology for the region, and implying an ergodic rainfall process. Slant-path attenuation statistics were estimated at 28.56 GHz by interfacing the measured rain-rate distributions at each of nine site locations with Crane's (1980) global model.

Goldhirsh, Julius↗
DOE OSTI2024

Regularized Differentiation for Bioburden Density Estimation in Planetary Protection

In this paper, we propose and investigate the performance of two novel shrinkage estimators for bioburden density estimation in planetary protection. The estimators are based on the regularized differentiation of a cumulative count of colony forming units collected throughout the data collecting session or the life cycle of the entire mission. The regularized differentiation recasts the problem of bioburden density estimation as a linear least squares problem. The least squares problem is then solved through regularization techniques, such as truncated singular value decomposition and penalized least squares. The regularization is necessary to avoid noise amplification during the differentiation of noisy data. The two regularization estimators are compared with four other commonly used estimators to simultaneously evaluate the means of multivariable independent Poisson distributions: the maximum likelihood, noninformative Bayes estimator with Jeffreys prior, Empirical Bayes using conjugate gamma-Poisson model with gamma parameters selected by method of moments, and the Clevenson-Zidek estimator. It is shown through computer-simulated data that the regularized differentiation based on ridge regression has the smallest mean-squared error among all estimators. The analysis of shrinkage mechanism implemented by regularized differentiation is performed, and it is shown that the regularized differentiation amounts to performing a weighted averaging of all the samples. The weights are determined by the regularization parameter automatically selected by the L-curve technique. Since the method of least squares makes no distributional assumptions about the data, it presents an attractive technique for bioburden density estimation when there are concerns about the misspecification of the distributional model. The paper concludes with the analysis of the bioburden data collected during InSight mission and directions for future work.

97 - MATHEMATICS AND COMPUTING↗
NASA NTRS2013

10 Yr Spatial and Temporal Trends of PM2.5 Concentrations in the Southeastern US Estimated Using High-resolution Satellite Data

Long-term PM2.5 exposure has been reported to be associated with various adverse health outcomes. However, most ground monitors are located in urban areas, leading to a potentially biased representation of the true regional PM2.5 levels. To facilitate epidemiological studies, accurate estimates of spatiotemporally continuous distribution of PM2.5 concentrations are essential. Satellite-retrieved aerosol optical depth (AOD) has been widely used for PM2.5 concentration estimation due to its comprehensive spatial coverage. Nevertheless, an inherent disadvantage of current AOD products is their coarse spatial resolutions. For instance, the spatial resolutions of the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Multiangle Imaging SpectroRadiometer (MISR) are 10 km and 17.6 km, respectively. In this paper, a new AOD product with 1 km spatial resolution retrieved by the multi-angle implementation of atmospheric correction (MAIAC) algorithm was used. A two-stage model was developed to account for both spatial and temporal variability in the PM2.5-AOD relationship by incorporating the MAIAC AOD, meteorological fields, and land use variables as predictors. Our study area is in the southeastern US, centered at the Atlanta Metro area, and data from 2001 to 2010 were collected from various sources. The model was fitted for each year individually, and we obtained model fitting R2 ranging from 0.71 to 0.85, MPE from 1.73 to 2.50 g m3, and RMSPE from 2.75 to 4.10 g m3. In addition, we found cross validation R2 ranging from 0.62 to 0.78, MPE from 2.00 to 3.01 g m3, and RMSPE from 3.12 to 5.00 g m3, indicating a good agreement between the estimated and observed values. Spatial trends show that high PM2.5 levels occurred in urban areas and along major highways, while low concentrations appeared in rural or mountainous areas. A time series analysis was conducted to examine temporal trends of PM2.5 concentrations in the study area from 2001 to 2010. The results showed that the PM2.5 levels in the study area followed a generally declining trend from 2001 to 2010 and decreased about 20 during the period. However, there was an exception of an increase in year 2005, which is attributed to elevated sulfate concentrations in the study area in warm months of 2005. An investigation of the impact of wild and prescribed fires on PM2.5 levels in 2007 suggests a positive relationship between them.

particulate matter (PM2.5)↗
NASA NTRS1991

The distribution of particulate material on Mars

The surface materials on Mars were extensively studied using a variety of spacecraft and Earth-based remote sensing observations. These measurements include: (1) diurnal thermal measurements, used to determine average particle size, rock abundance, and the presence of crusts; (2) radar observations, used to estimate the surface slope distributions, wavelength scale roughness, and density; (3) radio emission observations, used to estimate subsurface density; (4) broadband albedo measurements, used to study the time variation of surface brightness and dust deposition and removal; and (5) color observations, used to infer composition, mixing, and the presence of crusts. Remote sensing observations generally require some degree of modeling to interpret, making them more difficult to interpret than direct observations from the surface. They do, however, provide a means for examining the surface properties over the entire planet and a means of sampling varying depths within the regolith. Albedo and color observations only indicate the properties of the upper-most few microns, but are very sensitive to thin, sometimes emphemeral dust coatings. Thermal observations sample the upper skin depth, generally 2 to 10 cm. Rock abundance measurements give an indirect indication of surface mantling, where the absence of rocks suggests mantles of several meters. Finally, radar and radio emission data can penetrate several meters into the surface, providing an estimate of subsurface density and roughness.

Christensen, Philip R.↗
DOE OSTI2019

Sample Complexity of Power System State Estimation Using Matrix Completion

In this paper, we propose an analytical framework to quantify the amount of data samples needed to obtain accurate state estimation in a power system - a problem known as sample complexity analysis in computer science. Motivated by the increasing adoption of distributed energy resources into the distribution-level grids, it becomes imperative to estimate the state of distribution grids in order to ensure stable operation. Traditional power system state estimation techniques mainly focus on the transmission network which involve solving an overdetermined system and eliminating bad data. However, distribution networks are typically underdetermined due to the large number of connection points and high cost of pervasive installation of measurement devices. In this paper, we consider the recently proposed state-estimation method for underdetermined systems that is based on matrix completion. In particular, a constrained matrix completion algorithm was proposed, wherein the standard matrix completion problem is augmented with additional equality constraints representing the physics (namely power-flow constraints). We analyze the sample complexity of this general method by proving an upper bound on the sample complexity that depends directly on the properties of these constraints that can lower number of needed samples as compared to the unconstrained problem. To demonstrate the improvement that the constraints add to state estimation, we test the method on a 141-bus distribution network case study and compare it to the traditional least squares minimization state estimation method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Exact and efficient hybrid Monte Carlo algorithm for accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts

Single cells exhibit a significant amount of variability in transcript levels, which arises from slow, stochastic transitions between gene expression states. Elucidating the nature of these states and understanding how transition rates are affected by different regulatory mechanisms require state-of-the-art methods to infer underlying models of gene expression from single cell data. A Bayesian approach to statistical inference is the most suitable method for model selection and uncertainty quantification of kinetic parameters using small data sets. However, this approach is impractical because current algorithms are too slow to handle typical models of gene expression. To solve this problem, we first show that time-dependent mRNA distributions of discrete-state models of gene expression are dynamic Poisson mixtures, whose mixing kernels are characterized by a piecewise deterministic Markov process. Here, we combined this analytical result with a kinetic Monte Carlo algorithm to create a hybrid numerical method that accelerates the calculation of time-dependent mRNA distributions by 1000-fold compared to current methods. We then integrated the hybrid algorithm into an existing Monte Carlo sampler to estimate the Bayesian posterior distribution of many different, competing models in a reasonable amount of time. We demonstrate that kinetic parameters can be reasonably constrained for modestly sampled data sets if the model is known a priori. If there are many competing models, Bayesian evidence can rigorously quantify the likelihood of a model relative to other models from the data. We demonstrate that Bayesian evidence selects the true model and outperforms approximate metrics typically used for model selection.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype $\mathrm{lr(0)_n}$ nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. Importantly, the paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1985

Gamma-ray line emission from Al-26 produced by Wolf-Rayet stars

The recent satellite observations of the 1.8 MeV line from the decay of Al-26 has given a new impetus to the study of the nucleosynthesis of Al-26. The production and ejection of Al-26 by massive mass-losing stars (Of and WR stars) is discussed in the light of recent stellar models. The longitude distribution of the Al-26 gamma ray line emission produced by the galactic collection of WR stars is derived based on various estimates of their radial distribution. This longitude profile provides: (1) a specific signature of massive stars on the background of other potential Al-26 sources, as novae, supernovae, certain red giants and possibly AGB stars; and (2) a possible tool to improve the data analysis of the HEAO 3 and SMM experiments.

Prantzos, N.↗
DOE OSTI2020

Challenging a Global Land Surface Model in a Local Socio-Environmental System

Land surface models (LSMs) predict how terrestrial fluxes of carbon, water, and energy change with abiotic drivers to inform the other components of Earth system models. Here, we focus on a single human-dominated watershed in southwestern Michigan, USA. We compare multiple processes in a commonly used LSM, the Community Land Model (CLM), to observational data at the single grid cell scale. For model inputs, we show correlations (Pearson’s R) ranging from 0.46 to 0.81 for annual temperature and precipitation, but a substantial mismatch between land cover distributions and their changes over time, with CLM correctly representing total agricultural area, but assuming large areas of natural grasslands where forests grow in reality. For CLM processes (outputs), seasonal changes in leaf area index (LAI; phenology) do not track satellite estimates well, and peak LAI in CLM is nearly double the satellite record (5.1 versus 2.8). Estimates of greenness and productivity, however, are more similar between CLM and observations. Summer soil moisture tracks in timing but not magnitude. Land surface reflectance (albedo) shows significant positive correlations in the winter, but not in the summer. Looking forward, key areas for model improvement include land cover distribution estimates, phenology algorithms, summertime radiative transfer modelling, and plant stress responses.

54 ENVIRONMENTAL SCIENCES↗