Search NASA⌕ Search

SEARCH · Search NASA

Results for “imprecise probabilities”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Imprecise Probability Methods for Weapons UQ

Building on recent work in uncertainty quanti cation, we examine the use of imprecise probability methods to better characterize expert knowledge and to improve on misleading aspects of Bayesian analysis with informative prior distributions. Quantitative approaches to incorporate uncertainties in weapons certi cation are subject to rigorous external peer review, and in this regard, certain imprecise probability methods are well established in the literature and attractive. These methods are illustrated using experimental data from LANL detonator impact testing.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2015

Frequency analysis of uncertain structures using imprecise probability

Two new methods for finite element based frequency analysis of a structure with uncertainty are developed. An imprecise probability formulation based on enveloping p-boxes is used to quantify the uncertainty present in the mechanical characteristics of the structure. For each element, independent variations are considered. Using the two developed methods, P-box Frequency Analysis (PFA) and Interval Monte-Carlo Frequency Analysis (IMFA), sharp bounds on natural circular frequencies at different probability levels are obtained. These methods establish a framework for handling incomplete information in structural dynamics. Numerical example problems are presented that illustrate the capabilities of the new methods along with discussions on their computational efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

On the quantification and efficient propagation of imprecise probabilities with copula dependence

This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be mutually independent or correlated by a multivariate Gaussian distribution. However, this subjective assumption may introduce bias in the response estimate if the real dependence structure deviates from this assumption. In this work, we overcome this limitation by introducing a flexible copula dependence model to capture complex dependencies. Here, a hierarchical Bayesian multimodel approach is proposed to quantify uncertainty in dependence model-form and model parameters that result from small data sets. This approach begins by identifying, through Bayesian multimodel inference, a set of candidate marginal models and their corresponding model probabilities, and then estimating the uncertainty in the copula-based dependence structure, which is conditional on the marginals and their parameters. The overall uncertainties integrating marginals and copulas are probabilistically represented by an ensemble of multivariate candidate densities. A novel importance sampling reweighting approach is proposed to efficiently propagate the overall uncertainties through a computational model. Through an example studying the influence of constituent properties on the out-of-plane properties of transversely isotropic E-glass fiber composites, we show that the composite property with copula-based dependence model converges to the true estimate as data set size increases, while an independence or arbitrary Gaussian correlation assumption leads to a biased estimate.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

Effect of Epistemic Uncertainty Modeling Approach on Decision-Making: Example using Equipment Performance Indicator

Quantitative risk assessments are an integral part of risk-informed regulation of current and future nuclear plants in the U.S. The Bayesian approach to uncertainty, in which both stochastic and epistemic uncertainties are represented with precise probability distributions, is the standard approach to modeling uncertainties in such quantitative risk assessments. However, there are long-standing criticisms of the Bayesian approach to epistemic uncertainty from many perspectives, and a number of alternative approaches have been proposed. Among these alternatives, the most promising (and most rapidly developing) would appear to be the concept of imprecise probability. In this paper, we employ a performance indicator example to focus the discussion. We first give a short overview of the traditional Bayesian paradigm and review some its controversial aspects, for example, issues with so-called noninformative prior distributions. We then discuss how the imprecise probability approach treats these issues and compare it with two other approaches: sensitivity analysis and hierarchical Bayes modeling. We conclude with some practical implications for risk-informed decision making.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2020

Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling

Global Sensitivity Analysis (GSA) aims to understand the relative importance of uncertain input variables to model response. Conventional GSA involves calculating sensitivity (Sobol’) indices for a model with known model parameter distributions. However, model parameters are affected by aleatory and epistemic uncertainty, with the latter often caused by lack of data. In this paper, we propose a new framework to quantify uncertainty in probability model-form and model parameters resulting from small datasets and integrate these uncertainties into Sobol’ index estimates. First, the process establishes, through Bayesian multimodel inference, a set of candidate probability models and their associated probabilities. Imprecise Sobol’ indices are calculated from these probability models using an importance sampling reweighting approach. This results in probabilistic Sobol’ indices, whose distribution characterizes uncertainty in the sensitivity resulting from small dataset size. The imprecise Sobol’ indices thus provide a measure of confidence in the sensitivity estimate and, moreover, can be used to inform data collection efforts targeted to minimize the impact of uncertainties. Through an example studying the parameters of a Timoshenko beam, we show that these probabilistic Sobol’ indices converge to the true/deterministic Sobol’ indices as the dataset size increases and hence, distribution-form uncertainty reduces. The approach is then applied to assess the sensitivity of the out-of-plane properties of an E-glass fiber composite material to its constituent properties. This second example illustrates the approach for an important class of materials with wide-ranging applications when data may be lacking for some input parameters.

42 ENGINEERING↗
DOE OSTI2017

Sensitivity Analysis and Uncertainty Quantification for the LAMMPS Molecular Dynamics Simulation Code

We examine sensitivity analysis and uncertainty quantification for molecular dynamics simulation. Extreme (large or small) output values for the LAMMPS code often occur at the boundaries of input regions, and uncertainties in those boundary values are overlooked by common SA methods. Similarly, input values for which code outputs are consistent with calibration data can also occur near boundaries. Upon applying approaches in the literature for imprecise probabilities (IPs), much more realistic results are obtained than for the complacent application of standard SA and code calibration.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Probabilistic modeling and prediction of out-of-plane unidirectional composite lamina properties

Computational simulation provides an efficient means to predict the behavior of customized hybrid material configurations using validated, physics-based models. One limitation to this approach is the quality and quantity of available data to characterize the many constituent input properties. Therefore, a systematic approach to identify the most influential parameters on the hybrid behavior and quantify the corresponding uncertainty in predictive capabilities is required. Here, an approach using Bayesian multimodel inference and imprecise global sensitivity analysis is presented to investigate the effects of sparse constituent data on the prediction of composite material properties. The methodology allows the identification, using quantified uncertainties, of the most influential constituent material parameters for specified homogenized properties. This sensitivity analysis further enables a dimension reduction when assessing the influence of uncertainties on material properties and can be used to inform testing programs of the constituent properties that require additional testing/data collection in order to minimize uncertainty in macro-scale composite properties. The methodology is specifically demonstrated on the prediction and sensitivity analysis of out-of-plane mechanical properties of a unidirectional lamina.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Accommodating Uncertainty in Prior Distributions

A fundamental premise of Bayesian methodology is that a priori information is accurately summarized by a single, precisely de ned prior distribution. In many cases, especially involving informative priors, this premise is false, and the (mis)application of Bayes methods produces posterior quantities whose apparent precisions are highly misleading. We examine the implications of uncertainty in prior distributions, and present graphical methods for dealing with them.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

A new approach to analytic, non-perturbative and gauge-invariant QCD

Following a previous calculation of quark scattering in eikonal approximation, this paper presents a new, analytic and rigorous approach to the calculation of QCD phenomena. In this formulation a basic distinction between the conventional 'idealistic' description of QCD and a more 'realistic' description is brought into focus by a non-perturbative, gauge-invariant evaluation of the Schwinger solution for the QCD generating functional in terms of the exact Fradkin representations of Green's functional G{sub c}(x,y|A) and the vacuum functional L[A]. Because quarks exist asymptotically only in bound states, their transverse coordinates can never be measured with arbitrary precision; the non-perturbative neglect of this statement leads to obstructions that are easily corrected by invoking in the basic Lagrangian a probability amplitude which describes such transverse imprecision. The second result of this non-perturbative analysis is the appearance of a new and simplifying output called 'Effective Locality', in which the interactions between quarks by the exchange of a 'gluon bundle'-which 'bundle' contains an infinite number of gluons, including cubic and quartic gluon interactions-display an exact locality property that reduces the several functional integrals of the formulation down to a set of ordinary integrals. It should be emphasized that 'non-perturbative' here refers to the effective summation of all gluons between a pair of quark lines-which may be the same quark line, as in a self-energy graph-but does not (yet) include a summation over all closed-quark loops which are tied by gluon-bundle exchange to the rest of the 'Bundle Diagram'. As an example of the power of these methods we offer as a first analytic calculation the quark-antiquark binding potential of a pion, and the corresponding three-quark binding potential of a nucleon, obtained in a simple way from relevant eikonal scattering approximations. A second calculation, analytic, non-perturbative and gauge-invariant, of a nucleon-nucleon binding potential to form a model deuteron, will appear separately. - Highlights: Black-Right-Pointing-Pointer An analytic, non-perturbative and gauge-invariant formulation for QCD processes. Black-Right-Pointing-Pointer A new property called Effective Locality appears in the QCD fermionic amplitudes. Black-Right-Pointing-Pointer An effective quark-antiquark and 3-quark binding potential is obtained. Black-Right-Pointing-Pointer A single 'gluon bundle' replaces the sum of an infinite number of Feynman graphs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

The role of x-ray Swank factor in energy-resolving photon-counting imaging

Purpose: Energy-resolved x-ray imaging has the potential to improve contrast-to-noise ratio by measuring the energy of each interacting photon and applying optimal weighting factors. The success of energy-resolving photon-counting (EPC) detectors relies on the ability of an x-ray detector to accurately measure the energy of each interacting photon. However, the escape of characteristic emissions and Compton scatter degrades spectral information. This article makes the theoretical connection between accuracy and imprecision in energy measurements with the x-ray Swank factor for a-Se, Si, CdZnTe, and HgI{sub 2}-based detectors. Methods: For a detector that implements adaptive binning to sum all elements in which x-ray energy is deposited for a single interaction, energy imprecision is shown to depend on the Swank factor for a large element with x rays incident at the center. The response function for each converter material is determined using Monte Carlo methods and used to determine energy accuracy, Swank factor, and relative energy imprecision in photon-energy measurements. Results: For each material, at energies below the respective K edges, accuracy is close to unity and imprecision is only a few percent. Above the K-edge energies, characteristic emission results in a drop in accuracy and precision that depends on escape probability. In Si, and to some extent a-Se, Compton-scatter escape also degrades energy precision with increasing energy. The influence of converter thickness on energy accuracy and imprecision is modest for low-Z materials but becomes important when using high-Z materials at energies greater than the K-edge energies. Conclusions: Accuracy and precision in energy measurements by EPC detectors are determined largely by the energy-dependent x-ray Swank factor. Modest decreases in the Swank factor (5%-15%) result in large increases in relative imprecision (30%-40%).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2011

The Retrocausal Nature of Quantum Measurement Revealed by Partial and Weak Measurements

Quantum measurement is sometimes more effective when its result is not definite. Partial measurement turns the initial superposition not into a certain state but to a greater probability for it, enabling probing the quantum state in cases where complete measurement makes the noncommuting variables inaccessible. It also enables full quantum erasure that, unlike prevailing method, can be carried out even on recorded results. Aharonov's weak measurement is another method of imprecisely measuring quantum variables, outsmarting the uncertainty principle in even subtler ways. Happily, the two methods complement and corroborate one another in several interesting ways. We gedankenly apply these measurements to the EPR case. A pair of entangled particles undergoes more than one pair of partial and weak measurements, which, unlike complete measurements, leave them partially correlated. Their erasure is then shown to be as nonlocal as measurement itself. Surprisingly, the temporal relations between such measurements in the EPR setting do not follow the temporal sequence perceived by an external observer. For each particle, the measurements performed on the other operate as if they occurred (with signs reversed) in its own past, and in reversed order. This fully accords with Cramer's transactional interpretation and Aharonov's two state-vector formalism.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

A NEW METHOD TO DIRECTLY MEASURE THE JEANS SCALE OF THE INTERGALACTIC MEDIUM USING CLOSE QUASAR PAIRS

Although the baryons in the intergalactic medium (IGM) trace dark matter fluctuations on megaparsec scales, on smaller scales ∼100 kpc, fluctuations are suppressed because the finite temperature gas is pressure supported against gravity, analogous to the classical Jeans argument. This Jeans filtering scale, which quantifies the small-scale structure of the IGM, has fundamental cosmological implications. First, it provides a thermal record of heat injected by ultraviolet photons during cosmic reionization events, and thus constrains the thermal and reionization history of the universe. Second, the Jeans scale determines the clumpiness of the IGM, a critical ingredient in models of cosmic reionization. Third, it sets the minimum mass scale for gravitational collapse from the IGM, and hence plays a pivotal role in galaxy formation. Unfortunately, it is extremely challenging to measure the Jeans scale via the standard technique of analyzing purely longitudinal Lyα forest spectra, because the thermal Doppler broadening of absorption lines along the line-of-sight, is highly degenerate with Jeans smoothing. In this work, we show that the Jeans filtering scale can be directly measured by characterizing the coherence of correlated Lyα forest absorption in close quasar pairs, with separations small enough ∼100 kpc to resolve it. We present a novel technique for this purpose, based on the probability density function (PDF) of phase angle differences of homologous longitudinal Fourier modes in close quasar pair spectra. A Bayesian formalism is introduced based on the phase angle PDF, and Markov Chain Monte Carlo techniques are used to characterize the precision of a hypothetical Jeans scale measurement, and explore degeneracies with other thermal parameters governing the IGM. A semi-analytical model of the Lyα forest is used to generate a large grid (500) of thermal models from a dark matter only simulation. Our full parameter study indicates that a realistic sample of only 20 close quasar pair spectra can pinpoint the Jeans scale to ≅ 5% precision, independent of the amplitude T{sub 0} and slope γ of the temperature-density relation of the IGM T=T{sub 0}(ρ/ ρ-bar ){sup γ-1}. This exquisite sensitivity arises because even long-wavelength one-dimensional Fourier modes ∼10 Mpc, i.e., two orders of magnitude larger than the Jeans scale, are nevertheless dominated by projected small-scale three-dimensional (3D) power. Hence phase angle differences between all modes of quasar pair spectra actually probe the shape of the 3D power spectrum on scales comparable to the pair separation. We show that this new method for measuring the Jeans scale is unbiased and is insensitive to a battery of systematics that typically plague Lyα forest measurements, such as continuum fitting errors, imprecise knowledge of the noise level and/or spectral resolution, and metal-line absorption.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

SU-E-T-510: Mathematical Analysis of Approximate Biological Effective Dose (BED) Calculation for Multi-Phase Radiotherapy Treatment Plans

Purpose: There is growing interest about biological effective dose (BED) and its application in treatment plan evaluation due to its stronger correlation with treatment outcome. An approximate biological effective dose (BEDA) equation was introduced to simplify BED calculations by treatment planning systems in multi-phase treatments. The purpose of this work is to reveal its mathematical properties relative to the true, multi-phase BED (BEDT) equation. Methods: The BEDT equation was derived and used to reveal the mathematical properties of BEDA. MATLAB (MathWorks, Natick, MA) was used to simulate and analyze common and extreme clinical multi-phase cases. In those cases, percent error (Perror) and Bland-Altman analysis were used to study the significance of the inaccuracies of BEDA for different combinations of total doses, numbers of fractions, doses per fractions and α over β values. All the calculations were performed on a voxel-basis in order to study how dose distributions would affect the accuracy of BEDA. Results: When the voxel dose-per-fractions (DPF) delivered by both phases are equal, BEDA and BEDT are equal. In heterogeneous dose distributions, which significantly vary between the phases, there are fewer occurrences of equal DPFs and hence the imprecision of BEDA is greater. It was shown that as the α over β ratio increased the accuracy of BEDA would improve. Examining twenty-four cases, it was shown that the range of DPF ratios for a 3 Perror varied from 0.32 to 7.50Gy, whereas for Perror of 1 the range varied from 0.50 to 2.96Gy. Conclusion: The DPF between the different phases should be equal in order to render BEDA accurate. OARs typically receive heterogeneous dose distributions hence the probability of equal DPFs is low. Consequently, the BEDA equation should only be used for targets or OARs that receive uniform or very similar dose distributions by the different treatment phases.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2010

Evidence Theory Based Uncertainty Quantification in Radiological Risk due to Accidental Release of Radioactivity from a Nuclear Power Plant

Consequence of the accidental release of radioactivity from a nuclear power plant is assessed in terms of exposure or dose to the members of the public. Assessment of risk is routed through this dose computation. Dose computation basically depends on the basic dose assessment model and exposure pathways. One of the exposure pathways is the ingestion of contaminated food. The aim of the present paper is to compute the uncertainty associated with the risk to the members of the public due to the ingestion of contaminated food. The governing parameters of the ingestion dose assessment model being imprecise, we have approached evidence theory to compute the bound of the risk. The uncertainty is addressed by the belief and plausibility fuzzy measures.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

County-Level Climate Uncertainty for Risk Assessments: Volume 8 Appendix G - Historical Precipitation.

This report uses the CMIP5 series of climate model simulations to produce country- level uncertainty distributions for use in socioeconomic risk assessments of climate change impacts. It provides appropriate probability distributions, by month, for 169 countries and autonomous-areas on temperature, precipitation, maximum temperature, maximum wind speed, humidity, runoff, soil moisture and evaporation for the historical period (1976-2005), and for decadal time periods to 2100. It also provides historical and future distributions for the Arctic region on ice concentration, ice thickness, age of ice, and ice ridging in 15-degree longitude arc segments from the Arctic Circle to 80 degrees latitude, plus two polar semicircular regions from 80 to 90 degrees latitude. The uncertainty is meant to describe the lack of knowledge rather than imprecision in the physical simulation because the emphasis is on unfalsified risk and its use to determine potential socioeconomic impacts. The full report is contained in 27 volumes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

County-Level Climate Uncertainty for Risk Assessments: Volume 10 Appendix I - Historical Evaporation.

This report uses the CMIP5 series of climate model simulations to produce country- level uncertainty distributions for use in socioeconomic risk assessments of climate change impacts. It provides appropriate probability distributions, by month, for 169 countries and autonomous-areas on temperature, precipitation, maximum temperature, maximum wind speed, humidity, runoff, soil moisture and evaporation for the historical period (1976-2005), and for decadal time periods to 2100. It also provides historical and future distributions for the Arctic region on ice concentration, ice thickness, age of ice, and ice ridging in 15-degree longitude arc segments from the Arctic Circle to 80 degrees latitude, plus two polar semicircular regions from 80 to 90 degrees latitude. The uncertainty is meant to describe the lack of knowledge rather than imprecision in the physical simulation because the emphasis is on unfalsified risk and its use to determine potential socioeconomic impacts. The full report is contained in 27 volumes.

54 ENVIRONMENTAL SCIENCES↗