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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A non-commutative Bayes' theorem

Using a diagrammatic reformulation of Bayes' theorem, we provide a necessary and sufficient condition for the existence of Bayesian inference in the setting of finite-dimensional C* -algebras. In other words, we prove an analogue of Bayes' theorem in the joint classical and quantum context. Our analogue is justified by recent advances in categorical probability theory, which have provided an abstract formulation of the classical Bayes' theorem. In the process, we further develop non-commutative almost everywhere equivalence and illustrate its important role in non-commutative Bayesian inversion. The construction of such Bayesian inverses, when they exist, involves solving a positive semidefinite matrix completion problem for the Choi matrix. This gives a solution to the open problem of constructing Bayesian inversion for completely positive unital maps acting on density matrices that do not have full support. In conclusion, we illustrate how the procedure works for several examples relevant to quantum information theory.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Advancing the Theory of Nuclear Data Evaluations [Abstract]

We present recent advances in the R-matrix formalism as well as the Bayesian evaluation framework for improved nuclear data evaluations. The advances in the R matrix formalism include: 1) direct processes, 2) doorway, as well as multistep, processes, and 3) various forms of the Reich-Moore approximation for eliminated capture channels. Furthermore, to address unreasonably small posterior uncertainties often encountered in nuclear data evaluations of large data sets using the conventional form of the Bayes’ theorem, we introduce imperfections (of the data or the model) as a formal evaluation tool for taming the evaluated uncertainties in harmony with Bayes’ theorem. These theoretical advances were motivated by the nuclear data evaluations of differential resolved resonance cross section data using the code SAMMY, as well as the integral benchmark experiments using the SCALE code system, being performed at Oak Ridge National Laboratory for the Nuclear Criticality Safety Program. Some pedagogical applications of the new formalism, as well as a snapshot of the SAMMY modernization efforts, will be presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Bayesian Monte Carlo Evaluation of Imperfect (n, 233 U) Data and Model

Conventional nuclear data evaluation methods using generalized linear least squares make the following assumptions: prior and posterior probability distribution functions (PDFs) of all model parameters and data are normal (Gaussian); the linear approximation is sufficiently accurate to minimize the cost function (even for nonlinear models); the model (e.g., of neutron cross section) and experimental data (including covariance data) are without defect and prior PDFs of parameters and measured data are known perfectly. Neglect of covariance between model parameters and measured data in conventional evaluations contributes to imperfections. These assumptions are inherent to the generalized linear least squares minimization method commonly used for resolved resonance region neutron cross section evaluations but are often not justified due to the presence of non-normal PDFs, nonlinear models (e.g., R-matrix formalism), and inherent imperfections in data and models (e.g., imperfect covariance data). Here, these assumptions are removed in a mathematical framework of Bayes’ theorem, which is implemented using the Metropolis-Hastings Monte Carlo method. Most importantly, new parameters are introduced to parameterize discrepancies between the theoretical model and measured data to quantify judgement about discrepancies or imperfections in a reproducible manner. An evaluation of 233U in the eV region using the ENDF-B/VIII.0 library and transmission data (Guber et al.) is presented, and posterior parameters are compared to those obtained by conventional evaluation methods. This example illustrates the effects of removing the most harmful assumption: that of model-data perfection.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Generalized Bayesian Framework for Evaluation of Integral Benchmark Experiments [Slides]

This presentation is on generalized Bayesian framework for evaluation of integral benchmark experiments. This presentation starts off with assumptions and approximations used with Bayes Theorem. then an overview of approximations used by ORNL codes, and Generalized Bayesian Monto Carlo (GBMC). The presentation then details out a precise framework. This presentation then concludes with considerations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Advances in Nuclear Data Evaluation Theory for NCSP [Slides]

The generalized form of the Bayes’ Theorem improves UQ for NCSP of differential and/or integral data evaluations and of applications. It is being implemented in an API for use by SCALE, SAMMY, etc. Extended R-matrix formalism improves evaluations of RRR including direct reactions, direct capture, and the Reich-Moore approx., doorway state reactions with applications to RPI data on lead isotopes. Extended R-Matrix formalism will be implemented into SAMMY post modernization.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Determination of proton PDF uncertainties with Markov chain Monte Carlo

We present an analysis of parton distribution functions (PDFs) of the proton using Markov chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes’ theorem and, thus, provides a means to directly sample the underlying probability distribution—in this case, the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, 𝑊 and 𝑍 boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing one, e.g., to account for non-Gaussianity or inconsistencies of datasets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the Δ⁢𝜒 2 value corresponding to a given confidence level in the sample, which can, in turn, be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.

Risse, Peter Clemens [Universität Münster (Germany↗
DOE OSTI2020

A dataset of eco-evidence tools to inform early-stage environmental impact assessments of hydropower development

The datasets described herein provide the foundation for a decision support prototype (DSP) toolkit aimed at assisting stakeholders in determining evidence of which aspects of river ecosystems have been impacted by hydropower. The DSP toolkit and its application are presented and described in the article “Evidence-based indicator approach to guide preliminary environmental impact assessments of hydropower development” [1]. Development of the DSP and the output for decision support centralize around 42 river function indicators describing the dimensionality of river ecosystems through six main categories: biota and biodiversity, water quality, hydrology, geomorphology, land cover, and river connectivity. Three main tools are represented in the DSP: A science-based questionnaire (SBQ), an environmental envelope model (EEM), and a river function linkage assessment tool (RFLAT). The SBQ is a structured survey-style questionnaire whose objective is to provide evidence of which indicators have been impacted by hydropower. Based on a global literature review, 140 questions were developed from general hypotheses regarding the impacts of dams on rivers. The EEM is a model to predict the likelihood of hydropower impacting indicators based on a several variables. The intended use of the EEM is for situations of new hydropower development where results of the SBQ are incomplete or highly uncertain. The EEM was developed through the compilation of a dataset containing attributes of dams, reservoirs, and geospatial information on environmental concerns, which was combined with data on ecological indicators documented at those sites through literature review. The model operates through 247 “envelopes” and weighting factors, representing the individual effect of each variable on each indicator, all available through spreadsheets. Finally, the RFLAT is a tool to examine causal relationships amongst indicators. Inter-indicator relationships were hypothesized based on literature review and summarized into node and edge datasets to represent the structure of a graphical network. Bayes theorem was used estimate conditional probabilities of inter-indicator relationships based on the output of the SBQ. Nodes and edges were imported into R programming environment to visualize ecological indicator networks. The datasets can be expanded upon and enriched with more detailed questions for the SBQ, building upon the EEM with to develop more sophisticated models, and identifying new relationships for the RFALT. Additionally, once the tools are applied to numerous hydropower developments, the output of the tools (e.g. evidence of impacted indicators) becomes a very useful dataset for meta-analyses of hydropower impacts.

13 HYDRO ENERGY↗
DOE OSTI2023

Inverse aqueous transport modeling for emergency response

ALGE is a three-dimensional, finite-difference aqueous transport model that simulates pollutant fate and transport in lakes, rivers, bays, and estuaries by solving the prognostic equations of mass, momentum, and energy. Its current modeling capabilities include transport of dissolved tracer for a series of predefined basins across the continental United States. Recently, an inverse method (also known as backtracking) has been added to ALGE to provide a possible source of a pollutant should one be detected by a sensor in a body of water and a source is not known. This inverse method is a three step process that uses an algorithm to inverse the flow. We demonstrate the new model’s capabilities through simulating the 2021 Piney Point spill in Tampa Bay, Florida (USA). This involves moving tracer backwards from its detection points, encompassing a potential source area, and applying Bayes’ Theorem and $\frac{𝜒}{𝑄}$ to reduce the area within which the true source could be located.

hydrological modeling↗
DOE OSTI2025

Hierarchical Estimation For Planetary Protection

The software uses Bayes' theorem to describe the probability of an event based on prior knowledge of conditions that might be related to the event. The purpose of Bayesian analysis is to determine posterior probabilities based on prior probabilities where new information can be used in the decision-making process as additional data is gathered. The software will be used in Probabilistic Risk Assessments (PRAs) related to the Europa Clipper mission, which is one of NASA’s top priorities. Ultimately, the mission entails sending the Europa Clipper spacecraft to Jupiter’s Europa moon to orbit the planet and collect data for research and development. Europa is the smallest of the four Galilean moons orbiting Jupiter and is believed by researchers to be the most promising place to look for present-day environments suitable for life. Europa is thought to have an iron core, a rocky mantle, and a salt-water ocean covered by an ice-layered surface.

Gribok, Andrei [Idaho National Laboratory (INL), I↗
DOE OSTI2020

Parsimonious Inference Information-Theoretic Foundations for a Complete Theory of Machine Learning (CIS-LDRD Project 218313 Final Technical Report)

This work examines how we may cast machine learning within a complete Bayesian framework to quantify and suppress explanatory complexity from first principles. Our investigation into both the philosophy and mathematics of rational belief leads us to emphasize the critical role of Bayesian inference in learning well-justified predictions within a rigorous and complete extended logic. The Bayesian framework allows us to coherently account for evidence in the learned plausibility of potential explanations. As an extended logic, the Bayesian paradigm regards probability as a notion of degrees of truth. In order to satisfy critical properties of probability as a coherent measure, as well as maintain consistency with binary propositional logic, we arrive at Bayes' Theorem as the only justifiable mechanism to update our beliefs to account for empiracle evidence. Yet, in the machine learning paradigm, where explanations are unconstrained algorithmic abstractions, we arrive at a critical challenge: Bayesian inference requires prior belief. Conventional approaches fail to yield a consistent framework in which we could compare prior plausibility among the infinities of potential choices in learning architectures. The difficulty of articulating well-justified prior belief over abstract models is the provinence of memorization in traditional machine learning training practices. This becomes exceptionally problematic in the context of limited datasets, when we wish to learn justifiable predictions from only a small amount of data.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

Reliability and structural integrity

An analytic model is developed to calculate the reliability of a structure after it is inspected for cracks. The model accounts for the growth of undiscovered cracks between inspections and their effect upon the reliability after subsequent inspections. The model is based upon a differential form of Bayes' Theorem for reliability, and upon fracture mechanics for crack growth.

Davidson, J. R.↗
NASA NTRS1975

Reliability after inspection

The investigation is concerned with the derivation of relationships between the probability of having manufacturing defects, the probability of detecting a flaw, and the final reliability. Equations for the simple situation in which only one flaw can be present are used to introduce the relationships in a Bayes' theorem approach to the assessment of the final reliability. Situations which are prevalent in composites manufacturing are considered. Attention is given to a case involving the random occurrence of flaws on a laminate surface.

Davidson, J. R.↗
NASA NTRS1977

Bayesian estimation of crack initiation times from service data

Lockheed C-130 Hercules aircraft have during their service life been periodically inspected and growing cracks around rivet holes were recorded. This record has recently been used to determine the statistical distributions of crack initiation times and the distribution of initial crack sizes. When crack initiation times are calculated from such cracks, by backward extrapolation of the growth relation, the resulting distribution of crack initiation times will indicate a preponderance of short times to crack initiation. If however, such distributions are combined with the reliability of the inspection procedure, the statistical distribution of missed initiation times can be estimated. The method used is based on Bayes theorem which permits the calculation of the 'prior' distribution (initiation times before inspection) from a knowledge of the 'posterior' distribution (initiation times obtained from the inspection) and a 'likelihood function' (reliability of the inspection) procedure. The results indicate that during an early inspection a large percentage of initiation times will be missed and that the fraction of located initiation times increases during later inspections.

Heller, R. A.↗
NASA NTRS1976

Reliability and structural integrity

An analytic model is developed to calculate the reliability of a structure after it is inspected for cracks. The model accounts for the growth of undiscovered cracks between inspections and their effect upon the reliability after subsequent inspections. The model is based upon a differential form of Bayes' Theorem for reliability, and upon fracture mechanics for crack growth.

Davidson, J. R.↗
NASA NTRS1986

Induction of models under uncertainty

This paper outlines a procedure for performing induction under uncertainty. This procedure uses a probabilistic representation and uses Bayes' theorem to decide between alternative hypotheses (theories). This procedure is illustrated by a robot with no prior world experience performing induction on data it has gathered about the world. The particular inductive problem is the formation of class descriptions both for the tutored and untutored cases. The resulting class definitions are inherently probabilistic and so do not have any sharply defined membership criterion. This robot example raises some fundamental problems about induction; particularly, it is shown that inductively formed theories are not the best way to make predictions. Another difficulty is the need to provide prior probabilities for the set of possible theories. The main criterion for such priors is a pragmatic one aimed at keeping the theory structure as simple as possible, while still reflecting any structure discovered in the data.

Cheeseman, Peter↗
NASA NTRS1986

Automatic discovery of optimal classes

A criterion, based on Bayes' theorem, is described that defines the optimal set of classes (a classification) for a given set of examples. This criterion is transformed into an equivalent minimum message length criterion with an intuitive information interpretation. This criterion does not require that the number of classes be specified in advance, this is determined by the data. The minimum message length criterion includes the message length required to describe the classes, so there is a built in bias against adding new classes unless they lead to a reduction in the message length required to describe the data. Unfortunately, the search space of possible classifications is too large to search exhaustively, so heuristic search methods, such as simulated annealing, are applied. Tutored learning and probabilistic prediction in particular cases are an important indirect result of optimal class discovery. Extensions to the basic class induction program include the ability to combine category and real value data, hierarchical classes, independent classifications and deciding for each class which attributes are relevant.

Cheeseman, Peter↗