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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.

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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↗
NASA NTRS1990

Topics in inference and decision-making with partial knowledge

Two essential elements needed in the process of inference and decision-making are prior probabilities and likelihood functions. When both of these components are known accurately and precisely, the Bayesian approach provides a consistent and coherent solution to the problems of inference and decision-making. In many situations, however, either one or both of the above components may not be known, or at least may not be known precisely. This problem of partial knowledge about prior probabilities and likelihood functions is addressed. There are at least two ways to cope with this lack of precise knowledge: robust methods, and interval-valued methods. First, ways of modeling imprecision and indeterminacies in prior probabilities and likelihood functions are examined; then how imprecision in the above components carries over to the posterior probabilities is examined. Finally, the problem of decision making with imprecise posterior probabilities and the consequences of such actions are addressed. Application areas where the above problems may occur are in statistical pattern recognition problems, for example, the problem of classification of high-dimensional multispectral remote sensing image data.

Safavian, S. Rasoul↗
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 ↗
NASA NTRS1986

Dynamic remapping decisions in multi-phase parallel computations

The effectiveness of any given mapping of workload to processors in a parallel system is dependent on the stochastic behavior of the workload. Program behavior is often characterized by a sequence of phases, with phase changes occurring unpredictably. During a phase, the behavior is fairly stable, but may become quite different during the next phase. Thus a workload assignment generated for one phase may hinder performance during the next phase. We consider the problem of deciding whether to remap a paralled computation in the face of uncertainty in remapping's utility. Fundamentally, it is necessary to balance the expected remapping performance gain against the delay cost of remapping. This paper treats this problem formally by constructing a probabilistic model of a computation with at most two phases. We use stochastic dynamic programming to show that the remapping decision policy which minimizes the expected running time of the computation has an extremely simple structure: the optimal decision at any step is followed by comparing the probability of remapping gain against a threshold. This theoretical result stresses the importance of detecting a phase change, and assessing the possibility of gain from remapping. We also empirically study the sensitivity of optimal performance to imprecise decision threshold. Under a wide range of model parameter values, we find nearly optimal performance if remapping is chosen simply when the gain probability is high. These results strongly suggest that except in extreme cases, the remapping decision problem is essentially that of dynamically determining whether gain can be achieved by remapping after a phase change; precise quantification of the decision model parameters is not necessary.

Nicol, D. M.↗
NASA NTRS1999

Laboratory Astrophysics Under the Ultraviolet, Visible, and Gravitational Astrophysics Research Program

Space-borne facilities, such as the Hubble Space Telescope, the recent ORFEUS-SPAS II Shuttle mission, and the soon-to-be launched Far Ultraviolet Spectroscopic Explorer, are providing data at ultraviolet wavelengths of unprecedented quality for spectroscopic studies of many astronomical environments. The first step in the analysis of these data involves the derivation of abundances. Obtaining accurate abundances is possible only when the correspondence between line strength and abundance is well known. The conversion of line strength to abundance relies on knowledge of transition probabilities and oscillator strengths, often obtained from mean lives branching fractions. For many ultraviolet transitions, the necessary atomic and molecular data are either relatively imprecise or not available. Our program addresses this need for accurate oscillator strengths; our focus is on transitions that probe the nature and composition of the interstellar medium.

Federman, Steven R.↗
NASA NTRS2010

Robustness-Based Design Optimization Under Data Uncertainty

This paper proposes formulations and algorithms for design optimization under both aleatory (i.e., natural or physical variability) and epistemic uncertainty (i.e., imprecise probabilistic information), from the perspective of system robustness. The proposed formulations deal with epistemic uncertainty arising from both sparse and interval data without any assumption about the probability distributions of the random variables. A decoupled approach is proposed in this paper to un-nest the robustness-based design from the analysis of non-design epistemic variables to achieve computational efficiency. The proposed methods are illustrated for the upper stage design problem of a two-stage-to-orbit (TSTO) vehicle, where the information on the random design inputs are only available as sparse point and/or interval data. As collecting more data reduces uncertainty but increases cost, the effect of sample size on the optimality and robustness of the solution is also studied. A method is developed to determine the optimal sample size for sparse point data that leads to the solutions of the design problem that are least sensitive to variations in the input random variables.

Zaman, Kais↗
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↗
NASA NTRS1994

Spatial Acquisition in the Presence of Satellite Vibrations for Free Space Optical Communication Link

Laser communication systems offer distinct advantages over radio frequency based systems for near earth and particularly for deep space communicaiton links. Some of the advantages are smaller size, lower power requirements and higher data rates. However, laser beam widths are very narrow and require more precise pointing, acquisition and tracking (PAT) compared to RF communication sytems. In addition to imprecise knowledge of relative position and complex relative motion between the spacecrafts, the problem of pointing and acquisition is complicated by vibrations present in the spacecraft. This paper analyzes the impact of satellite vibration on acquisition time and acquisition probability for a charge coupled device (CCD) based acquisition scheme.

laser↗