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All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Bayesian Analysis of the Power Spectrum of the Cosmic Microwave Background

There is a wealth of cosmological information encoded in the spatial power spectrum of temperature anisotropies of the cosmic microwave background. The sky, when viewed in the microwave, is very uniform, with a nearly perfect blackbody spectrum at 2.7 degrees. Very small amplitude brightness fluctuations (to one part in a million!!) trace small density perturbations in the early universe (roughly 300,000 years after the Big Bang), which later grow through gravitational instability to the large-scale structure seen in redshift surveys... In this talk, I will discuss a Bayesian formulation of this problem; discuss a Gibbs sampling approach to numerically sampling from the Bayesian posterior, and the application of this approach to the first-year data from the Wilkinson Microwave Anisotropy Probe. I will also comment on recent algorithmic developments for this approach to be tractable for the even more massive data set to be returned from the Planck satellite.

Bayesian inference↗
DOE OSTI2025

Fully Bayesian Analysis With Model Inadequacy Correction For Nuclear Graphite Property Models With Hierarchical Variance Structure

Nuclear-grade graphites are extensively utilized in the core designs of various advanced nuclear reactors. Within the reactor environment, graphite is subjected to prolonged exposure to extreme conditions, including high temperatures, radiation, and potentially molten salt and oxygen. Such exposure can induce several degradation mechanisms in graphite, such as nonuniform volumetric strains caused by irradiation and thermal expansion, leading to stresses that may compromise the performance of graphite components. Assessing component integrity, forecasting component performance over the reactor's lifespan, and developing design standards necessitate robust tools for predicting fracture initiation and propagation in graphite structural components within nuclear reactors. This code enables the Bayesian calibration of properties for nuclear-grade graphites. Using a hierarchical Bayesian approach, multiple experimental data sources are combined to develop Gaussian process models for the properties. Using the Kennedy O'Hagan framework, the uncertainties due inadequacies in the model and the inherent spread in the experimental data are quantified.

Dhulipala, Som Lakshmi NarasimhaLakshmi Narasimha ↗
DOE OSTI2024

Bayesian Analysis of TRISO Fuel: Quantifying Model Inadequacy, Incorporating Lower-Length-Scale Effects, and Developing Parallel Active Learning Capabilities

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel-cycle systems. This program has been providing engineering-scale support for the continued development of BISON, a high-fidelity, high-resolution fuel performance tool. Fuel behavior in nuclear reactors is governed by a complex network of mechanisms that interact with various other physics aspects in the reactor system. Any model developed to represent fuel behavior will likely be idealized, resulting in uncertainties when comparing their predictions against the observed data. In Fiscal Year (FY)-23, we initiated the Uncertainty Quantification (UQ) work by using Bayesian methods to establish a level of model trustworthiness and further improve it, with a particular emphasis on TRI-Structural isOtropic (TRISO) nuclear fuel. This year, we further expanded on that UQ work by investigating an approach to quantifying model inadequacy and accounting for lower-length scale (LLS) effects in TRISO silver (Ag) release modeling. Furthermore, we are implementing parallel active learning capabilities to reduce the computational cost (i.e., required computational resources and elapsed time) of performing UQ. Specifically, we utilized The Kennedy O’Hagan framework for Bayesian uncertainty quantification (KOH) to account for model inadequacy in TRISO Ag release predictions made by BISON. The KOH framework represents an improvement over the standard Bayesian framework used in FY-23. Explicitly accounting for model inadequacy in the Bayesian framework helps establish the level of experimental noise uncertainty in the Advanced Gas Reactor (AGR) data. We compared the inverse UQ results obtained from both the standard Bayesian and KOH frameworks in light of the AGR-2/3/4 data, and also compared the predictive UQ results obtained from these two frameworks in light of the AGR-1 data. Next, we investigated the impact of considering LLS effects in the Ag release simulations. We developed an expanded database of LLS simulated effective diffusivities for Ag, covering a wide range of microstructures and temperatures. Using this database, we developed a framework for incorporating LLS effects into the engineering-scale Ag release UQ. We developed both parametric and non-parametric approaches for bridging the length scales. We then investigated the inverse UQ results in light of the AGR-2/3/4 data and the predictive UQ results in light of the AGR-1 data, and compared the LLS-informed approach and the Arrhenius equation, which does not include microstructure information. Finally, we discussed implementing parallel active learning capabilities in the Multiphysics Object Oriented Simulation Environment (MOOSE)/BISON to reduce the computational cost (i.e., computational resources and elapsed time) of Bayesian UQ. For verification purposes, we first tested these new capabil ities on a species interaction problem. We then demonstrated them on the TRISO Ag release application, showing that parallel active learning capabilities can enhance the accuracy of UQ while also substantially reducing the computational cost in comparison to the reference methods developed in FY-23.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Evaluating the limitations of Bayesian metabolic control analysis

Bayesian Metabolic Control Analysis (BMCA) is a promising framework for inferring metabolic control coefficients in data-limited scenarios, combining Bayesian inference with linear-logarithmic (lin-log) rate laws. These metabolic control coefficients quantify how changes in enzyme activities affect steady-state fluxes and metabolite concentrations across a metabolic network. However, its predictive accuracy and limitations remain underexplored. This study systematically evaluates BMCA’s ability to infer elasticity values, flux control coefficients (FCC), and concentration control coefficients (CCC) under varying data availability conditions using three synthetic metabolic network models. We demonstrate that BMCA predictions are highly dependent on the inclusion of flux and enzyme concentration data, with the omission of these datasets leading to severe inaccuracies. In our synthetic, enzyme-perturbation datasets, external metabolite concentrations had minimal impact and, in some cases, their exclusion improved predictions; when external-nutrient perturbations were introduced and those concentrations were observed, gains were at most modest. Additionally, we find that posterior estimation with both ADVI and HMC can underestimate large-magnitude elasticities in our synthetic settings, with ADVI showing somewhat higher variance under strong up-regulation; thus, recovering |elasticity| ≳ 1.5 remains challenging regardless of the inference engine. ADVI also fails to accurately infer allosteric interactions, even when regulatory effects are strong. While BMCA maintains reasonable accuracy in partially recovering the rankings of the highest FCC values, its estimates of absolute values remain constrained by prior assumptions and data limitations. Our findings reveal the BMCA algorithm’s strengths and weaknesses, providing guidance on its application in metabolic engineering, and highlighting the need for methodological refinements to enhance its predictive capabilities.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2013

Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations

This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors. We present a simple nonparametric modeling technique and an algorithm implementing it-an improved and generalized version of Bayesian Blocks [Scargle 1998]-that finds the optimal segmentation of the data in the observation interval. The structure of the algorithm allows it to be used in either a real-time trigger mode, or a retrospective mode. Maximum likelihood or marginal posterior functions to measure model fitness are presented for events, binned counts, and measurements at arbitrary times with known error distributions. Problems addressed include those connected with data gaps, variable exposure, extension to piece- wise linear and piecewise exponential representations, multivariate time series data, analysis of variance, data on the circle, other data modes, and dispersed data. Simulations provide evidence that the detection efficiency for weak signals is close to a theoretical asymptotic limit derived by [Arias-Castro, Donoho and Huo 2003]. In the spirit of Reproducible Research [Donoho et al. (2008)] all of the code and data necessary to reproduce all of the figures in this paper are included as auxiliary material.

signal detection↗
NASA NTRSDate not supplied

Enhancing Fault Isolation for Health Monitoring of Electric Aircraft Propulsion by Embedding Failure Mode and Effect Analysis into Bayesian Networks

This paper describes a fault isolation approach for electric powertrains of unmanned aerial vehicles. The approach leverages the combination of failure mode and effect analysis (FMEA) and Bayesian networks, thus introducing depend-ability structures into a diagnostic framework. Faults and failure events from the FMEA are mapped within a Bayesian network, where network edges replicate the links embedded within FMEAs. This framework helps the fault isolation process by identifying the probability of occurrence of specific faults or root causes given evidence observed through sensor signals. The framework is applied to an electric power-train system of a small, rotary-wing unmanned aerial vehicle, demonstrating how a Bayesian network enhanced by FMEA helps disambiguate between root causes of incipient failures, which would otherwise be considered as equally probable.

Fault Isolation↗
DOE OSTI2025

Improving Trustworthiness of Data-Driven Power Grid Contingency Analysis With Bayesian Residual Graph Neural Networks

The evolving energy landscape requires novel tools to efficiently perform contingency analysis and reliability assessment of power grids, potentially in real-time. The high computational cost of traditional power flow solvers limits their applicability in practice. Machine learning (ML) surrogates such as deep neural networks (NNs) accelerate power flow solvers computations, enabling high-order contingency analysis and real-time decision-making by learning highly nonlinear functions and integrating grid topology via graph architectures. However, (graph) NNs lack predictive power away from training data and do not provide predictive confidence estimates. Here, we present a Bayesian residual graph NN that integrates knowledge from low-fidelity data via residual training and embeds granular quantification of uncertainties, improving trustworthiness critical for high-consequence decision-making. Applying Bayesian concepts to NNs is challenging due to the high-dimensionality of both the parameter space, complicating derivation of a meaningful prior, and the output space in large grid systems, requiring enhanced techniques to assess the predicted high-dimensional uncertainties. Our contributions include: (1) Deriving a prior for fully connected and graph NNs that leverages low-fidelity data to guide mean predictions and appropriately control prior predictive uncertainty. (2) Integrating this prior within an ensembling with anchoring scheme for efficient approximate posterior inference. (3) Deriving enhanced metrics to assess accuracy of both the mean and uncertainty predictions in high dimensions, appropriately accounting for correlations propagated through graph layers. The resulting Bayesian residual graph NN is tested on a contingency analysis task for 14-bus and 118-bus grids.

24 - POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Bayesian inference analysis of jet quenching using inclusive jet and hadron suppression measurements

The JETSCAPE Collaboration reports a new determination of the jet transport parameter $\hat{q}$ in the quark-gluon plasma (QGP) using Bayesian inference, incorporating all available inclusive hadron and jet yield suppression data measured in heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC). This multi-observable analysis extends the previously published JETSCAPE Bayesian inference determination of $\hat{q}$, which was based solely on a selection of inclusive hadron suppression data. jetscape is a modular framework incorporating detailed dynamical models of QGP formation and evolution, and jet propagation and interaction in the QGP. Virtuality-dependent partonic energy loss in the QGP is modeled as a thermalized weakly coupled plasma, with parameters determined from Bayesian calibration using soft-sector observables. This Bayesian calibration of $\hat{q}$ utilizes active learning, a machine-learning approach, for efficient exploitation of computing resources. The experimental data included in this analysis span a broad range in collision energy and centrality, and in transverse momentum. In order to explore the systematic dependence of the extracted parameter posterior distributions, several different calibrations are reported, based on combined jet and hadron data; on jet or hadron data separately; and on restricted kinematic or centrality ranges of the jet and hadron data. Tension is observed in comparison of these variations, providing new insights into the physics of jet transport in the QGP and its theoretical formulation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1972

Evaluation of errors in prior mean and variance in the estimation of integrated circuit failure rates using Bayesian methods

The critical point of any Bayesian analysis concerns the choice and quantification of the prior information. The effects of prior data on a Bayesian analysis are studied. Comparisons of the maximum likelihood estimator, the Bayesian estimator, and the known failure rate are presented. The results of the many simulated trails are then analyzed to show the region of criticality for prior information being supplied to the Bayesian estimator. In particular, effects of prior mean and variance are determined as a function of the amount of test data available.

Fletcher, B. C.↗
NASA NTRS2019

OGLE-2014-BLG-0962 and a Comparison of Galactic Model Priors to Microlensing Data

OGLE-2014-BLG-0962 (OB140962) is a stellar binary microlensing event that was well covered by observations from the Spitzer satellite as well as ground-based surveys. Modeling yields a unique physical solution: a mid-M+M-dwarf binary with M(prim) = 0.20 ± 0.01 M(☉) and M(sec) = 0.16 ± 0.01 M(☉), with projected separation of 2.0 ± 0.3 au. The lens is only D(LS) = 0.41 ± 0.06 kpc in front of the source, making OB140962 a bulge lens and the most distant Spitzer binary lens to date. In contrast, because the Einstein radius (θ(E) = 0.143 ± 0.007 mas) is unusually small, a standard Bayesian analysis, conducted in the absence of parallax information, would predict a brown dwarf binary. We compare the results of Bayesian analysis using two commonly used Galactic model priors to the measured values for a set of Spitzer lenses. We find all models tested predict lens properties consistent with the Spitzer data. Furthermore, we illustrate the methodology for probing the Galactic distribution of planets by comparing the cumulative distance distribution of the Spitzer two-body lenses to that of the Spitzer single lenses.

Yutong Shan↗
NASA NTRS1973

Bayesian estimation of life parameters in the Weibull distribution.

Development of a Bayesian analysis of the scale and shape parameters in the Weibull distribution and the corresponding reliability function with respect to the usual life-testing procedures. For the scale parameter theta, Bayesian estimates of theta and reliability are obtained for the uniform, exponential, and inverted gamma prior probability densities. Bhattacharya's results (1967) for the one-parameter exponential life-testing distribution are reduced to a special case of these results. A fully Bayesian analysis of both the scale and shape parameters is developed by assuming independent prior distributions; since in the latter case, analytical tractability is not possible, Bayesian estimates are obtained through a conjunction of Monte Carlo simulation and numerical-integration techniques. In both cases, a computer simulation is carried out, and a comparison is made between the Bayesian and the corresponding minimum-variance unbiased, or maximum likelihood, estimates. As expected, the Bayesian estimates are superior.

Canavos, G. C.↗
DOE OSTI2024

Global constraint on the jet transport coefficient from single-hadron, dihadron, and γ -hadron spectra in high-energy heavy-ion collisions

Modifications of large transverse momentum single-hadron, dihadron, and γ -hadron spectra in relativistic heavy-ion collisions are direct consequences of parton-medium interactions in the quark-gluon plasma (QGP). The interaction strength and underlying dynamics can be quantified by the jet transport coefficient q ̂ . We carry out the first global constraint on q ̂ using a next-to-leading order pQCD parton model with higher-twist parton energy loss and combining world experimental data on single-hadron, dihadron, and γ -hadron suppression at both RHIC and LHC energies with a wide range of centralities. The global Bayesian analysis using the information field (IF) priors provides the most stringent constraint on q ̂ ( T ) . We demonstrate in particular the progressive constraining power of the IF Bayesian analysis on the strong temperature dependence of q ̂ using data from different centralities and colliding energies. We also discuss the advantage of using both inclusive and correlation observables with different geometric biases. As a verification, the obtained q ̂ ( T ) is shown to describe data on single-hadron anisotropy at high transverse momentum well. Predictions for future jet quenching measurements in oxygen-oxygen collisions are also provided. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRSDate not supplied

Adding GPU Support to the Markov Chain Monte Carlo Code Catmip

In geophysics, we are confronted with many under-determined inverse problems. For example, all of our observations of earthquakes are made at the Earth’s surface. So, when we try to infer how slip during an earthquake evolves in space and time, we find that there are many potential slip histories that are consistent with our limited observations and our understanding of earthquake physics. One way to approach these problems is with Bayesian analysis which allows us to infer the ensemble of all potential slip models that satisfy the observations and our prior knowledge of earthquake physics. In Bayesian analysis, our prior knowledge is known as the prior probability density function or prior PDF, the fit to the data is known as the data likelihood, and the target PDF that satisfies both the prior PDF and data likelihood is known as the posterior PDF. However, simulating the posterior PDF typically requires using Markov Chain Monte Carlo (MCMC) to draw tens of billions of random realizations of earthquake slip models, which may not be computationally feasible. To make this and similar geophysical inversions computationally tractable, we developed the Cascading Adaptive Transitional Metropolis In Parallel (CATMIP) algorithm. CATMIP is an efficient parallel Markov Chain Monte Carlo (MCMC) sampler that is used for model fitting and uncertainty quantification in geophysics. Example use cases are earthquake rupture modeling, determining mineral composition on Mars, reconstructing the history of ocean salinity, and historical earthquake relocation. CATMIP employs many parallel instances of the Metropolis algorithm for sampling in a transitioning framework. Transitioning is a process in which a set of random samples at equilibrium with a known probability density function (PDF) are used as seeds for the Markov chains to sample successive target PDFs that incrementally move the distribution from the starting seeds to the final desired PDF that describes the relative plausibility of potential values for the model parameters. The algorithm is implemented as a Master-Worker model employing MPI for communication. The worker processes are loosely coupled with global parameters periodically optimized by the master process. This provides a very high amount of parallelism with little communication between updates. During the presentation we will discuss the history of the algorithm and elaborate the earthquake rupture modeling use case for the CATMIP package. Our first step toward GPU optimization was to optimize the code for the CPU. CPU profiling revealed that most of the compute time is spent in calls to level 2 BLAS routines and calls to GSL random number generators. We revised the algorithm to employ level 3 BLAS routines instead. In our presentation we will describe how this was accomplished. Adding GPU support to CATMIP consisted mostly of replacing the calls to GSL with calls to GPU vendor-provided library routines. A small number of loops were directly implemented in CUDA. In the presentation will provide implementation details. Finally, we will discuss methods for profiling and opportunities for further optimizing GPU execution. By creating a code with the flexibility to run on either a CPU or GPU architecture, CATMIP can be used on systems ranging from large CPU-based HPC environments to single servers with GPU acceleration and everything in between.

HECC↗
NASA NTRS2021

OGLE-2018-BLG-1185b: A Low-mass Microlensing Planet Orbiting a Low-mass Dwarf

We report an analysis of the planetary microlensing event OGLE-2018-BLG-1185, which was observed by a large number of ground-based telescopes and by the Spitzer Space Telescope. The ground-based light curve indicates a low planet–host star mass ratio ofq=(6.9±0.2)×10−5, which is near the peak of the wide-orbit exoplanet mass-ratio distribution. We estimate the host star and planet masses with a Bayesian analysis using the measured angular Einstein radius under the assumption that stars of all masses have an equal probability of hosting the planet. The flux variation observed by Spitzer is marginal, but still places a constraint on the microlens parallax. Imposing a conservative constraint that this flux variation should beΔfSpz<4 instrumental flux units yields a host mass of=-+MM0.37 host 0.210.35 and a planet mass of =-+ÅmM8.4p4.77.9. A Bayesian analysis including the full parallax constraint from Spitzer suggests smaller host star and planet masses of =-+MM0.091 host 0.0180.064 and =-+ÅmM2.1p0.41.5, respectively. Future high-resolution imaging observations with the Hubble Space Telescope or Extremely Large Telescope could distinguish between these two scenarios and help reveal the planetary system properties in more detail.

Gravitational microlensing↗
DOE OSTI2025

Kβ X-ray Emission Spectra Analysis Using Bayesian Optimization

The Kβ X-ray emission spectrum of 3 d transition metals is rich with electronic and structural information due to strong exchange interactions with the valence shell of the metal, and has become crucial for understanding their spin and oxidation states. The spectrum is commonly treated using crystal-field multiplet theory, a semi-empirical theory that uses tunable parameters to control the strength of the effects present in X-ray emission spectroscopy (XES). However, determining the experimental values of these parameters remains a challenge. We present a methodology that applies Bayesian optimization to crystal-field multiplet theory to determine parameter values. The algorithm is tested on the X-ray emission spectra of a collection of Mn, Co, and Ni oxides. We are able to find optimal values for the four most impactful parameters: Slater−Condon reduction factors F dd , F pd , and G pd , and crystal field splitting 10 Dq . The algorithm produces significantly improved accuracy compared to current analysis methods, and probes interparameter dependencies by modeling the error landscape. This advancement enhances XES analysis by offering an approach of obtaining quantitative electronic structural information on 3 d transition metal valence shells, facilitating applications across various scientific fields.

Bayesian optimization↗