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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

A Guide to the Literature on Learning Graphical Models

This literature review discusses different methods under the general rubric of learning Bayesian networks from data, and more generally, learning probabilistic graphical models. Because many problems in artificial intelligence, statistics and neural networks can be represented as a probabilistic graphical model, this area provides a unifying perspective on learning. This paper organizes the research in this area along methodological lines of increasing complexity.

Buntine, Wray L.↗
DOE OSTI2024

Improved Statistical Analysis for the Neutrinoless Double-Beta Decay Matrix Element of 136Xe

Neutrinoless double beta decay nuclear matrix element (M0ν) for 136Xe was recently analyzed using a statistical approach (Phys. Rev. C 107, 045501 (2023)). In the analysis, three initial shell model effective Hamiltonians were randomly altered, and their results for 23 measured observables were used to infer credibility for the M0ν nuclear matrix element (NME) based on a Bayesian Model Averaging approach. In that analysis, a reasonable Gamow-Teller quenching factor of 0.7 was assumed for each starting effective Hamiltonian. Given that the result of the statistical analysis was sensible to this choice, we are here improving that analysis by assuming that the Gamow-Teller quenching factor is also randomly chosen within reasonabe limits for all three starting Hamiltonians. The outcomes are slightly higher expectation values and uncertainties for the M0ν NME.

Astronomy & Astrophysics↗
NASA NTRS1992

The statistical analysis of circadian phase and amplitude in constant-routine core-temperature data

Accurate estimation of the phases and amplitude of the endogenous circadian pacemaker from constant-routine core-temperature series is crucial for making inferences about the properties of the human biological clock from data collected under this protocol. This paper presents a set of statistical methods based on a harmonic-regression-plus-correlated-noise model for estimating the phases and the amplitude of the endogenous circadian pacemaker from constant-routine core-temperature data. The methods include a Bayesian Monte Carlo procedure for computing the uncertainty in these circadian functions. We illustrate the techniques with a detailed study of a single subject's core-temperature series and describe their relationship to other statistical methods for circadian data analysis. In our laboratory, these methods have been successfully used to analyze more than 300 constant routines and provide a highly reliable means of extracting phase and amplitude information from core-temperature data.

NASA Discipline Regulatory Physiology↗
DOE OSTI2025

Greedy emulators for nuclear two-body scattering

Applications of reduced basis method emulators are increasing in low-energy nuclear physics because they enable fast and accurate sampling of high-fidelity calculations, enabling robust uncertainty quantification. Here, in this paper, we develop, implement, and test two model-driven emulators based on the (Petrov-)Galerkin projection using the prototypical test case of two-body scattering with the Minnesota potential and a more realistic local chiral potential. The high-fidelity scattering equations are solved with the matrix Numerov method, a reformulation of the popular Numerov recurrence relation for solving special second-order differential equations as a linear system of coupled equations. A novel error estimator based on reduced-space residuals is applied to an active learning approach (a greedy algorithm) to choosing training samples (“snapshots”) for the emulator and contrasted with a proper orthogonal decomposition (POD) approach. Both approaches allow for computationally efficient offline-online decompositions, but the greedy approach requires many fewer snapshot calculations. These developments set the groundwork for emulating scattering observables based on chiral nucleon-nucleon and three-nucleon interactions and optical models, where computational speed-ups are necessary for Bayesian uncertainty quantification. Our emulators and error estimators are widely applicable to linear systems.

Bayesian methods↗
DOE OSTI2026

Active learning emulators for nuclear two-body scattering in momentum space

In this work we extend the active learning emulators for two-body scattering in coordinate space with error estimation, recently developed by Maldonado et al. [Phys. Rev. C 112, 024002], to coupled-channel scattering in momentum space. Our full-order model (FOM) solver is based on the Lippmann-Schwinger integral equation for the scattering t-matrix as opposed to the radial Schrödinger equation. We use (Petrov-)Galerkin projections and high-fidelity calculations at a few snapshots across the parameter space of the interaction to construct efficient reduced-order models (ROMs), trained by a greedy algorithm for locally optimal snapshot selection. Both the FOM solver and the corresponding ROMs are implemented efficiently in Python using Google's JAX library. We present results for emulating scattering phase shifts in coupled and uncoupled channels and cross sections, and assess the accuracy of the developed ROMs and their computational speedup factors. We also develop emulator error estimation for both the t-matrix and the total cross section. The software framework for reproducing and extending our results is publicly available. Together with our recent advances in developing active-learning emulators for three-body scattering, these emulator frameworks set the stage for full Bayesian calibrations of chiral nuclear interactions and optical models against scattering data with quantified emulator errors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2002

Incorporating Biological Knowledge into Evaluation of Casual Regulatory Hypothesis

Biological data can be scarce and costly to obtain. The small number of samples available typically limits statistical power and makes reliable inference of causal relations extremely difficult. However, we argue that statistical power can be increased substantially by incorporating prior knowledge and data from diverse sources. We present a Bayesian framework that combines information from different sources and we show empirically that this lets one make correct causal inferences with small sample sizes that otherwise would be impossible.

Chrisman, Lonnie↗
NASA NTRS2010

JSC Safety and Mission Assurance Data Analysis Overview

These slides describe the data analysis methods that are used to determine inputs for probabilistic risk models supporting the Space Shuttle Program. Other applications can follow a similar path probably using different data sources. Statistical approaches are different and not addressed here. Topics included here: 1) Prior Distribution; 2) Likelihood Data; 3) Bayesian Updating; and 4) Uncertainty and Error. Note: This is a high-level discussion and is not intended to be a tutorial.

Roelant, Henk↗
NASA NTRS2013

The Gemini Planet-Finding Campaign: The Frequency of Giant Planets Around Debris Disk Stars

We have completed a high-contrast direct imaging survey for giant planets around 57 debris disk stars as part of the Gemini NICI Planet-Finding Campaign. We achieved median H-band contrasts of 12.4 mag at 0farcs5 and 14.1 mag at 1'' separation. Follow-up observations of the 66 candidates with projected separation <500 AU show that all of them are background objects. To establish statistical constraints on the underlying giant planet population based on our imaging data, we have developed a new Bayesian formalism that incorporates (1) non-detections, (2) single-epoch candidates, (3) astrometric and (4) photometric information, and (5) the possibility of multiple planets per star to constrain the planet population. Our formalism allows us to include in our analysis the previously known β Pictoris and the HR 8799 planets. Our results show at 95% confidence that <13% of debris disk stars have a ≥5 M Jup planet beyond 80 AU, and <21% of debris disk stars have a ≥3 M Jup planet outside of 40 AU, based on hot-start evolutionary models. We model the population of directly imaged planets as d(sq.)N/dMda ∝ m(sub α) a(sup β), where m is planet mass and a is orbital semi-major axis (with a maximum value of a(sub max)). We find that β < -0.8 and/or α > 1.7. Likewise, we find that β < -0.8 and/or a(sub max) < 200 AU. For the case where the planet frequency rises sharply with mass (α > 1.7), this occurs because all the planets detected to date have masses above 5 M(sub Jup), but planets of lower mass could easily have been detected by our search. If we ignore the β Pic and HR 8799 planets (should they belong to a rare and distinct group), we find that <20% of debris disk stars have a ≥3 M(sub Jup) planet beyond 10 AU, and β < -0.8 and/or α < -1.5. Likewise, β < -0.8 and/or a(sub max) < 125 AU. Our Bayesian constraints are not strong enough to reveal any dependence of the planet frequency on stellar host mass. Studies of transition disks have suggested that about 20% of stars are undergoing planet formation; our non-detections at large separations show that planets with orbital separation >40 AU and planet masses >3 M(sub Jup) do not carve the central holes in these disks.

Bayesian formalism↗
DOE OSTI2026

Forecasting generative amplification

Generative networks are perfect tools to enhance the speed and precision of LHC simulations. Especially when generating events beyond the size of the training dataset, it is important to understand their statistical precision. We present two complementary methods to estimate the amplification factor without large holdout datasets. Averaging amplification uses Bayesian networks or ensembling to estimate amplification from the precision of integrals over given phase-space volumes. Differential amplification uses hypothesis testing to quantify amplification without any resolution loss. Applied to state-of-the-art event generators, both methods indicate that amplification is already possible in specific regions of phase space.

Bahl, Henning [Heidelberg Univ. (Germany)] (ORCID:↗
DOE OSTI2024

Localization of infrasonic sources via Bayesian back projection

SUMMARY A Bayesian framework is investigated for event-specific localization of infrasonic sources using back projection ray tracing. Direction-of-arrival information from array-based detection analysis is used to initialize a back projection ray path originating from the detecting array location and quantifying propagation characteristics from hypothetical source locations. The Fisher statistic, computed from the array’s beam coherence, is mapped into uncertainty in the launch angles of the ray path. Auxiliary parameters previously introduced for solving the Transport equation to compute geometric spreading along ray paths are used to map uncertainty in the ray launch angles into spatial and temporal uncertainties in the ray path. An atmospheric ensemble approach is applied to account for atmospheric uncertainty, and the relation between uncertainties in the atmospheric state and confidence in estimated localization are evaluated using several ensembles with specified variances. The method is evaluated using a synthetic event in the western United States constructed via forward propagation simulations as well as a single-station, multi-arrival detection from a surface explosion in the western United States. Localization results using this event-specific approach are more accurate and exhibit improved precision than existing Bayesian localization methods that leverage generalized, pre-computed propagation statistics.

58 GEOSCIENCES↗
DOE OSTI2026

Hierarchical Gaussian Random Field Sampling for Multilevel Markov Chain Monte Carlo: Coupling Stochastic Partial Differential Equation and the Karhunen–Loève Decomposition

This work introduces structure preserving hierarchical decompositions for sampling Gaussian random fields (GRFs) within the context of multilevel Bayesian inference in high-dimensional space. Existing scalable hierarchical sampling methods, such as those based on stochastic partial differential equations (SPDEs), often reduce the dimensionality of the sample space at the cost of accuracy of inference. Other approaches, such that those based on Karhunen-Loève (KL) expansions, offer sample space dimensionality reduction but sacrifice GRF representation accuracy and ergodicity of the Markov chain Monte Carlo (MCMC) sampler and are computationally expensive for high-dimensional problems. The proposed method integrates the dimensionality reduction capabilities of KL expansions with the scalability of SPDE-based sampling, thereby providing a robust, unified framework for high-dimensional uncertainty quantification (UQ) that is scalable and accurate, preserves ergodicity, and offers dimensionality reduction of the sample space. The hierarchy in our multilevel algorithm is derived from the geometric multigrid hierarchy. By constructing a hierarchical decomposition that maintains the covariance structure across the levels in the hierarchy, the approach enables efficient coarse-to-fine sampling while ensuring that all samples are drawn from the desired distribution. The effectiveness of the proposed method is demonstrated on a benchmark subsurface flow problem, demonstrating its effectiveness in improving computational efficiency and statistical accuracy. Furthermore, our proposed technique is more efficient and accurate and displays better convergence properties than existing methods for high-dimensional Bayesian inference problems.

Gaussian random fields↗
DOE OSTI2025

A Bayesian Framework for Spectral Reprojection

Abstract Fourier partial sum approximations yield exponential accuracy for smooth and periodic functions, but produce the infamous Gibbs phenomenon for non-periodic ones. Spectral reprojection resolves the Gibbs phenomenon by projecting the Fourier partial sum onto a Gibbs complementary basis, often prescribed as the Gegenbauer polynomials. Noise in the Fourier data and the Runge phenomenon both degrade the quality of the Gegenbauer reconstruction solution, however. Motivated by its theoretical convergence properties, this paper proposes a new Bayesian framework for spectral reprojection, which allows a greater understanding of the impact of noise on the reprojection method from a statistical point of view. We are also able to improve the robustness with respect to the Gegenbauer polynomials parameters. Finally, the framework provides a mechanism to quantify the uncertainty of the solution estimate.

Li, Tongtong (ORCID:0000000276644764)↗
DOE OSTI2024

Visible core spectroscopy at Wendelstein 7-X

This paper presents an overview of recent hardware extensions and data analysis developments to the Wendelstein 7-X visible core spectroscopy systems. These include upgrades to prepare the in-vessel components for long-pulse operation, nine additional spectrometers, a new line of sight array for passive spectroscopy, and a coherence imaging charge exchange spectroscopy diagnostic. Progress in data analysis includes ion temperatures and densities from multiple impurity species, a statistical comparison with x-ray crystal spectrometer measurements, neutral density measurements from thermal passive Balmer-alpha emission, and a Bayesian analysis of active hydrogen emission, which is able to infer electron density and main ion temperature profiles.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS2007

Uncertainty Management for Diagnostics and Prognostics of Batteries using Bayesian Techniques

Uncertainty management has always been the key hurdle faced by diagnostics and prognostics algorithms. A Bayesian treatment of this problem provides an elegant and theoretically sound approach to the modern Condition- Based Maintenance (CBM)/Prognostic Health Management (PHM) paradigm. The application of the Bayesian techniques to regression and classification in the form of Relevance Vector Machine (RVM), and to state estimation as in Particle Filters (PF), provides a powerful tool to integrate the diagnosis and prognosis of battery health. The RVM, which is a Bayesian treatment of the Support Vector Machine (SVM), is used for model identification, while the PF framework uses the learnt model, statistical estimates of noise and anticipated operational conditions to provide estimates of remaining useful life (RUL) in the form of a probability density function (PDF). This type of prognostics generates a significant value addition to the management of any operation involving electrical systems.

Saha, Bhaskar↗
NASA NTRS2016

Uncertainty Estimates of Psychoacoustic Thresholds Obtained from Group Tests

Adaptive psychoacoustic test methods, in which the next signal level depends on the response to the previous signal, are the most efficient for determining psychoacoustic thresholds of individual subjects. In many tests conducted in the NASA psychoacoustic labs, the goal is to determine thresholds representative of the general population. To do this economically, non-adaptive testing methods are used in which three or four subjects are tested at the same time with predetermined signal levels. This approach requires us to identify techniques for assessing the uncertainty in resulting group-average psychoacoustic thresholds. In this presentation we examine the Delta Method of frequentist statistics, the Generalized Linear Model (GLM), the Nonparametric Bootstrap, a frequentist method, and Markov Chain Monte Carlo Posterior Estimation and a Bayesian approach. Each technique is exercised on a manufactured, theoretical dataset and then on datasets from two psychoacoustics facilities at NASA. The Delta Method is the simplest to implement and accurate for the cases studied. The GLM is found to be the least robust, and the Bootstrap takes the longest to calculate. The Bayesian Posterior Estimate is the most versatile technique examined because it allows the inclusion of prior information.

Rathsam, Jonathan↗
NASA NTRS2016

Confidence Intervals for Laboratory Sonic Boom Annoyance Tests

Commercial supersonic flight is currently forbidden over land because sonic booms have historically caused unacceptable annoyance levels in overflown communities. NASA is providing data and expertise to noise regulators as they consider relaxing the ban for future quiet supersonic aircraft. One deliverable NASA will provide is a predictive model for indoor annoyance to aid in setting an acceptable quiet sonic boom threshold. A laboratory study was conducted to determine how indoor vibrations caused by sonic booms affect annoyance judgments. The test method required finding the point of subjective equality (PSE) between sonic boom signals that cause vibrations and signals not causing vibrations played at various amplitudes. This presentation focuses on a few statistical techniques for estimating the interval around the PSE. The techniques examined are the Delta Method, Parametric and Nonparametric Bootstrapping, and Bayesian Posterior Estimation.

Rathsam, Jonathan↗
DOE OSTI2026

Quantifying uncertainty in physics-based predictions of rare-isotope production cross sections via Bayesian-inspired model averaging across nuclear mass tables

Accurate prediction of fragmentation cross sections is essential for rare-isotope beam production, planning new-isotope searches, and designing experiments to study the most exotic regions of the nuclear chart. However, existing reaction models and phenomenological cross-section parametrizations often exhibit significant deviations over broad regions of mass and charge. In this work, a Bayesian-inspired model-averaging framework is developed to combine abrasion-ablation (AA) calculations based on multiple nuclear mass tables into a single statistically weighted estimate. For the calibrated systems, the model weights are assigned empirically according to the relative quality of fit to measured cross sections, thereby reducing systematic model bias while preserving the underlying physics content of the AA description. The weights are constrained using proton-rich fragmentation data for the 78 Kr and 124 Xe projectiles. The resulting parameter trends are then propagated to the 92 Mo and 144 Sm systems through a controlled scaling procedure. In the present implementation, the excitation-energy prescription is fixed, while the averaging is performed across nuclear-mass inputs; the framework provides both weighted cross sections and associated uncertainty estimates. Applied to proton-rich fragmentation, the present approach provides a practical basis for interpolation and limited extrapolation in regions relevant to rare-isotope production. The resulting predictions are used to assess the production of very proton-rich nuclei, and candidate new isotopes are discussed.

Bayesian methods↗