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NASA NTRS2008

Joint Bayesian Component Separation and CMB Power Spectrum Estimation

We describe and implement an exact, flexible, and computationally efficient algorithm for joint component separation and CMB power spectrum estimation, building on a Gibbs sampling framework. Two essential new features are (1) conditional sampling of foreground spectral parameters and (2) joint sampling of all amplitude-type degrees of freedom (e.g., CMB, foreground pixel amplitudes, and global template amplitudes) given spectral parameters. Given a parametric model of the foreground signals, we estimate efficiently and accurately the exact joint foreground- CMB posterior distribution and, therefore, all marginal distributions such as the CMB power spectrum or foreground spectral index posteriors. The main limitation of the current implementation is the requirement of identical beam responses at all frequencies, which restricts the analysis to the lowest resolution of a given experiment. We outline a future generalization to multiresolution observations. To verify the method, we analyze simple models and compare the results to analytical predictions. We then analyze a realistic simulation with properties similar to the 3 yr WMAP data, downgraded to a common resolution of 3 deg FWHM. The results from the actual 3 yr WMAP temperature analysis are presented in a companion Letter.

numerical↗

NASA NTRS1994

Operations for Learning with Graphical Models

This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian net- works, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. These operations adapt existing techniques from statistics and automatic differentiation to graphs. Two standard algorithm schemes for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximization algorithm. Some algorithms are developed in this graphical framework including a generalized version of linear regression, techniques for feed-forward networks, and learning Gaussian and discrete Bayesian networks from data. The paper concludes by sketching some implications for data analysis and summarizing some popular algorithms that fall within the framework presented. The main original contributions here are the decomposition techniques and the demonstration that graphical models provide a framework for understanding and developing complex learning algorithms.

Buntine, Wray L.↗

DOE OSTI2025

Measurement of $\nu_\mu$ CC Interactions With Two-Proton Final State in MINERvA

This dissertation presents a measurement of charged–current (CC) muon–neutrino interactions with exactly two protons and no pions in the final state (CC~$2p\,0\pi$), using data collected by the MINERvA detector in the NuMI medium–energy beam at Fermilab. Such two–proton topologies are a sensitive probe of nuclear dynamics in the few–GeV regime, including multi–nucleon correlations (npnh, notably $2p2h$) and intranuclear final–state interactions (FSI) such as pion absorption and nucleon rescattering. A precise experimental characterization of these processes is essential both for neutrino–interaction theory and for reducing systematic uncertainties in oscillation experiments that rely on accurate modeling of neutrino–nucleus interactions. Events are selected by requiring a $\nu_\mu$ CC interaction with a reconstructed $\mu^-$ and two proton tracks originating from a common vertex in MINERvA’s finely segmented scintillator tracker, with no reconstructed mesons. Muon charge and momentum are constrained by matching to the MINOS Near Detector, while proton identification exploits energy–loss profiles and stopping–proton features. Backgrounds from pion–producing channels that enter the signal region through FSI or reconstruction effects are constrained with data–driven sidebands (Michel–electron and isolated–cluster “blob” samples) and tuned via a simultaneous fit across signal and sideband regions. To correct detector resolution and acceptance effects, the analysis employs iterative Bayesian unfolding with extensive validation: statistical pseudo–experiments, and robustness checks against generator systematic “universes” and additional strong shape warps. Single–differential cross sections are reported for three observables tailored to the two–proton final state: the opening–angle cosine $\cos\!\left(\theta_{pp}\right)$, the leading–proton momentum, and the subleading–proton momentum. Systematic uncertainties include contributions from neutrino flux, interaction modeling (e.g., npnh and resonance parameters, pion FSI), and detector response (calibration, reconstruction efficiencies). The resulting distributions provide targeted constraints on the interplay of multi–nucleon dynamics and FSI that shape CC~$2p\,0\pi$ final states on hydrocarbon. Comparisons to modern GENIE–based simulations highlight kinematic regions where model components require refinement. These measurements thus inform generator tuning and improve the reliability of neutrino–energy reconstruction strategies for current and future long–baseline oscillation programs.

Syrotenko, Vladyslav S. [Tufts U.]↗

DOE OSTI2025

Enhancing approximate modular Bayesian inference by emulating the conditional posterior

In modular Bayesian analyses, complex models are composed of distinct modules, each representing different aspects of the data or prior information. In this context, fully Bayesian approaches can sometimes lead to undesirable feedback between modules, compromising the integrity of the inference. The “cut-distribution” prevents unwanted influence between modules by “cutting” feedback. The direct sampling (DS) algorithm is standard practice for approximating the cut-distribution, but it can be computationally intensive, especially when the number of imputations required is large. An enhanced method is proposed, the Emulating the Conditional Posterior (ECP) algorithm, which leverages emulation to increase the number of imputations. Through numerical experiment it is demonstrated that the ECP algorithm outperforms the traditional DS approach in terms of accuracy and computational efficiency, particularly when resources are constrained. Here, it is also shown how the DS algorithm can be improved using ideas from design of experiments. Some practical recommendations are given for algorithm choice in modular Bayesian analyses.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Direct nonparametric multimessenger constraints on the equation of state of cold dense nuclear matter

We utilize the now substantial amount of astrophysical observations of neutron stars (NSs), along with perturbative quantum chromodynamics (pQCD) calculations at high density, to directly constrain the NS equation of state (EOS). To this end, we construct nonparametric EOS priors by using Gaussian processes trained on 75 EOSs, which include models with either hadrons, hyperons, or quarks at high densities. We create a prior using the full EOS sample (model agnostic), and one prior for each EOS family to test model discrimination. We introduce a novel inference approach, which allows the simultaneous sampling of intrinsic and extrinsic parameters of binary NS mergers, as well as a nonparametric equation of state. We showcase this method in a Bayesian updating scheme by first performing a complete analysis of the binary NS merger event GW170817 with minimal assumptions, and sequentially adding information from x-ray and radio NS observations, along with pQCD calculations. Besides providing standard constraints, such as the pressure at twice nuclear saturation density 𝑝⁡(2⁢𝜌 sat ) = 4.3$^{+0.6}_{−0.6}$ × 10 34 dyne/cm 2 , at 95% confidence level, for the model agnostic prior, our methodology shows how the choice of EOS families used in conditioning changes the inferred astrophysical properties of the EOS, namely tidal deformability and maximum supported NS mass. We find hyperonic priors predicting higher tidal deformabilities for a 1.4⁢𝑀 ⊙ NS, and hadronic priors being preferred by the considered astrophysical data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2007

Bayesian Analysis 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! Experiments designed to map the microwave sky are returning a flood of data (time streams of instrument response as a beam is swept over the sky) at several different frequencies (from 30 to 900 GHz), all with different resolutions and noise properties. The resulting analysis challenge is to estimate, and quantify our uncertainty in, the spatial power spectrum of the cosmic microwave background given the complexities of "missing data", foreground emission, and complicated instrumental noise. Bayesian formulation of this problem allows consistent treatment of many complexities including complicated instrumental noise and foregrounds, and can be numerically implemented with Gibbs sampling. Gibbs sampling has now been validated as an efficient, statistically exact, and practically useful method for low-resolution (as demonstrated on WMAP 1 and 3 year temperature and polarization data). Continuing development for Planck - the goal is to exploit the unique capabilities of Gibbs sampling to directly propagate uncertainties in both foreground and instrument models to total uncertainty in cosmological parameters.

methods - statistical↗

NASA NTRS2021

The M-dwarf Ultraviolet Spectroscopic Sample. I. Determining Stellar Parameters for Field Stars

Accurate stellar properties are essential for precise stellar astrophysics and exoplanetary science. In the M-dwarf regime, much effort has gone into defining empirical relations that can use readily accessible observables to assess physical stellar properties. Often, these relations for the quantity of interest are cast as a nonlinear function of available data; in Bayesian modeling, however, the reverse is needed. In this article, we introduce a new Bayesian framework to self-consistently and simultaneously apply multiple empirical calibrations to fully characterize the mass, luminosity, radius, and effective temperature of a field age M-dwarf. This framework includes a new M-dwarf mass–radius relation with a scatter of 3.1% at fixed mass. We further introduce the M-dwarf Ultraviolet Spectroscopic Sample (MUSS), and apply our methodology to provide consistent stellar parameters for these nearby low-mass stars, selected as having available spectroscopic data in the ultraviolet. These targets are of interest largely as either exoplanet hosts or benchmarks in multiwavelength stellar activity. We use the field MUSS stars to define a low-mass main sequence in the solar neighborhood through Gaussian Process (GP) regression. These results enable us to empirically measure a feature in the GP derivative at M ⊙ that indicates where the MUSS transitions from fully to partly convective interiors.

J. Sebastian Pineda↗

NASA NTRS1979

Orbit/attitude estimation with Landsat-1 and -2 landmark data

The accuracy of spacecraft orbit and attitude determination is investigated using Landsat-1 and -2 picture data. The data consists of ground control points, of known geodetic coordinates, which are identified on a series of Landsat pictures. Both sequential (extended Kalman filter) and batch (nonlinear Bayesian weighted least-squares) estimation techniques have been implemented in two software systems. Discussion of these systems includes a system overview, mathematical formulation, and sample numerical results. Particular emphasis is given to the application of a spectral analysis technique to derive spacecraft attitude models.

Hall, D. L.↗

NASA NTRS2015

Parameter Estimation for Compact Binaries with Ground-Based Gravitational-Wave Observations Using the LALInference

The Advanced LIGO and Advanced Virgo gravitational wave (GW) detectors will begin operation in the coming years, with compact binary coalescence events a likely source for the first detections. The gravitational waveforms emitted directly encode information about the sources, including the masses and spins of the compact objects. Recovering the physical parameters of the sources from the GW observations is a key analysis task. This work describes the LALInference software library for Bayesian parameter estimation of compact binary signals, which builds on several previous methods to provide a well-tested toolkit which has already been used for several studies. We show that our implementation is able to correctly recover the parameters of compact binary signals from simulated data from the advanced GW detectors. We demonstrate this with a detailed comparison on three compact binary systems: a binary neutron star (BNS), a neutron star - black hole binary (NSBH) and a binary black hole (BBH), where we show a cross-comparison of results obtained using three independent sampling algorithms. These systems were analysed with non-spinning, aligned spin and generic spin configurations respectively, showing that consistent results can be obtained even with the full 15-dimensional parameter space of the generic spin configurations. We also demonstrate statistically that the Bayesian credible intervals we recover correspond to frequentist confidence intervals under correct prior assumptions by analysing a set of 100 signals drawn from the prior. We discuss the computational cost of these algorithms, and describe the general and problem-specific sampling techniques we have used to improve the efficiency of sampling the compact binary coalescence (CBC) parameter space.

gravitational wave↗

NASA NTRS2005

Gesture Based Control and EMG Decomposition

This paper presents two probabilistic developments for use with Electromyograms (EMG). First described is a new-electric interface for virtual device control based on gesture recognition. The second development is a Bayesian method for decomposing EMG into individual motor unit action potentials. This more complex technique will then allow for higher resolution in separating muscle groups for gesture recognition. All examples presented rely upon sampling EMG data from a subject's forearm. The gesture based recognition uses pattern recognition software that has been trained to identify gestures from among a given set of gestures. The pattern recognition software consists of hidden Markov models which are used to recognize the gestures as they are being performed in real-time from moving averages of EMG. Two experiments were conducted to examine the feasibility of this interface technology. The first replicated a virtual joystick interface, and the second replicated a keyboard. Moving averages of EMG do not provide easy distinction between fine muscle groups. To better distinguish between different fine motor skill muscle groups we present a Bayesian algorithm to separate surface EMG into representative motor unit action potentials. The algorithm is based upon differential Variable Component Analysis (dVCA) [l], [2] which was originally developed for Electroencephalograms. The algorithm uses a simple forward model representing a mixture of motor unit action potentials as seen across multiple channels. The parameters of this model are iteratively optimized for each component. Results are presented on both synthetic and experimental EMG data. The synthetic case has additive white noise and is compared with known components. The experimental EMG data was obtained using a custom linear electrode array designed for this study.

Wheeler, Kevin R.↗

NASA NTRS2005

An Ensemble Approach to Building Mercer Kernels with Prior Information

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly dimensional feature space. we describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using pre-defined kernels. These data adaptive kernels can encode prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. Specifically, we demonstrate the use of the algorithm in situations with extremely small samples of data. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS) and demonstrate the method's superior performance against standard methods. The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains templates for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic-algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code.

Srivastava, Ashok N.↗

NASA NTRS2022

Updated Orbital Monitoring and Dynamical Masses for Nearby M-dwarf Binaries

Young M-type binaries are particularly useful for precise isochronal dating by taking advantage of their extended pre-main sequence evolution. Orbital monitoring of these low-mass objects becomes essential in constraining their fundamental properties, as dynamical masses can be extracted from their Keplerian motion. Here, we present the combined efforts of the AstraLux Large Multiplicity Survey, together with a filler sub-programme from the SpHere INfrared Exoplanet (SHINE) project and previously unpublished data from the FastCam lucky imaging camera at the Nordical Optical Telescope (NOT) and the NaCo instrument at the Very Large Telescope (VLT). Building on previous work, we use archival and new astrometric data to constrain orbital parameters for 20 M-type binaries. We identify that eight of the binaries have strong Bayesian probabilities and belong to known young moving groups (YMGs). We provide a first attempt at constraining orbital parameters for 14 of the binaries in our sample, with the remaining six having previously fitted orbits for which we provide additional astrometric data and updated Gaia parallaxes. The substantial orbital information built up here for four of the binaries allows for direct comparison between individual dynamical masses and theoretical masses from stellar evolutionary model isochrones, with an additional three binary systems with tentative individual dynamical mass estimates likely to be improved in the near future. We attained an overall agreement between the dynamical masses and the theoretical masses from the isochrones based on the assumed YMG age of the respective binary pair. The two systems with the best orbital constrains for which we obtained individual dynamical masses, J0728 and J2317, display higher dynamical masses than predicted by evolutionary models.

Astrometry / binaries↗

NASA NTRSDate not supplied

Application of a Bayesian Framework for Plasticity Model Selection

Interpretable Machine Learning (IML) has performed well when tasked with deriving constitutive material models. However, IML has been shown to prefer models that overfit noise in data, which tends to lead to bloat and a decrease in interpretability. Due to these issues, the ability of IML to reliably derive models that fit the data and are both interpretable and generalizable is limited. A method developed recently has shown promise to improve upon traditional IML by using a Bayesian fitness definition for the evolution of free-form models with non-deterministic parameters. This framework was developed for genetic-programming-based symbolic regression(GPSR) and involves model parameter estimation using Sequential Monte Carlo sampling (SMC).The method has demonstrated a reduction in bloat when dealing with noisy data in comparison to conventional GPSR. The results of this framework applied to stress-strain data for copper show models that more effectively predict the experimental data better than was previously shown with GPSR.

plasticity↗

DOE OSTI2025

A Behavioral Robotics Approach to Radiation Mapping Using Adaptive Sampling

Radiation mapping is a desirable task to automate because of the inherent risks involved and its tedious nature. A novel system was designed to address this by combining various existing technologies, utilizing behavior-based robotics and Bayesian optimization. The system uses a quadruped robot equipped with a manipulator and gamma detector to take measurements at locations that are selected based on the uncertainty of a surrogate model used to estimate the true radiation field. The robot uses input from the world with depth cameras to avoid collisions with the robot’s body, and unreachable points for the end effector are addressed by both allowing for a soft collision with the environment to occur, prompting the system to abandon that point, and varying the exploration tendency of the optimization based on consecutive collisions. This approach provides unique traversability and adaptability over other strategies in the literature. Experiments were performed by placing a Cesium-137 source on the ground and varying geometric setups and an optimization parameter demonstrating the adaptability to diverse environments and the increased robustness resulting from the designed behavior. The results additionally demonstrate that dynamically adjusting the optimization algorithm’s exploration tendency based on the arm’s collision history improves the system’s ability to navigate cluttered environments and construct accurate radiation maps without getting stuck in unreachable areas.

Adams, Joel↗

DOE OSTI2024

Characterizing the Uncertainty of Measurement of Traceable Isotope Ratios with Bayesian Statistical Techniques

Analytical techniques such as multicollector—inductively coupled plasma—mass spectrometry (MC-ICP-MS) are routinely employed at SRNL, other National Laboratories, and in academia to determine the precise isotopic composition of diverse natural and anthropogenic samples (e.g., rocks and nuclear materials). Quantifying and reporting uncertainty in such analyses, while regularly performed, have a rigorous statistical foundation. The Guide to the Expression of Uncertainty in Measurement 4 (GUM) outlines conventional techniques used to assess such uncertainty. As the accessibility and speed of statistical computing increase, there is a need to modernize conventional techniques. For example, Supplement 1 to the 3rd to the GUM suggests the use of approximation methods as an updated approach to the GUM.

McLarty, Ellis C.↗

DOE OSTI2025

LABQ3: Bayesian method for quantification of mineral compositions and nano-scale elemental mapping of 3D synchrotron XCT data

Quantitative analysis of mineral compositions is essential in understanding geochemical, mineralogical and environmental processes. Fine-resolution 3D imaging is widely done using synchrotron X-ray computed tomography (XCT), but existing analyses are limited to visualization and segmentation. This paper presents a new method, Linear Attenuation Bayesian Quantitative 3D-mapper (LABQ3), based on the linearity of X-ray attenuation with respect to elemental concentrations. To address the random variability in attenuation measurements, LABQ3 employs Bayesian decision theory to minimize classification error, using reference attenuation distributions from scans of pure mineral standards. To demonstrate LABQ3 and test its performance, we studied precipitated carbonate samples. XCT scans were done at multiple energies using the transmission X-ray microscope (TXM) at beamline 32-ID-C of the Advanced Photon Source at Argonne National Laboratory. The reconstructed 3D images have a voxel size of 20 nm. Analyses revealed rich nano-scale compositional heterogeneity within individual particles. A mixture of calcium and cadmium produced an overall stoichiometric composition of (Ca 0.78 ,Cd 0.22 )CO 3 , with some voxels containing nearly pure CdCO 3 . The addition of zinc led to an overall stoichiometric composition of 33% Ca, 28% Cd, 39% Zn, with a nearly pure CaCO 3 core and compositional zonation through the rim. These compositional gradients are related to temporal sequences of carbonate mineral formation where Cd precipitated at the beginning in (Ca,Cd)CO 3 , while Cd and Zn precipitated at the end in (Ca, Cd,Zn)CO 3 . Results differ from bulk analyses using Inductively Coupled Plasma-Mass Spectrometry (ICP-MS), showing that LABQ3 provides particle-specific insights. LABQ3 distinguishes itself by quantifying chemical compositions along a continuum, making it different from XCT analyses based on segmentation. LABQ3 allows simultaneous acquisition of morphology and chemical composition in 3D, facilitating the interpretation of chemical gradients of trace elements, quantification of solid solution compositions, inferences about temporal sequences of mineral precipitation, and addressing other concerns about solid-phase chemistry.

58 GEOSCIENCES↗

NASA NTRS2004

Perceptual learning through optimization of attentional weighting: human versus optimal Bayesian learner

Human performance in visual detection, discrimination, identification, and search tasks typically improves with practice. Psychophysical studies suggest that perceptual learning is mediated by an enhancement in the coding of the signal, and physiological studies suggest that it might be related to the plasticity in the weighting or selection of sensory units coding task relevant information (learning through attention optimization). We propose an experimental paradigm (optimal perceptual learning paradigm) to systematically study the dynamics of perceptual learning in humans by allowing comparisons to that of an optimal Bayesian algorithm and a number of suboptimal learning models. We measured improvement in human localization (eight-alternative forced-choice with feedback) performance of a target randomly sampled from four elongated Gaussian targets with different orientations and polarities and kept as a target for a block of four trials. The results suggest that the human perceptual learning can occur within a lapse of four trials (<1 min) but that human learning is slower and incomplete with respect to the optimal algorithm (23.3% reduction in human efficiency from the 1st-to-4th learning trials). The greatest improvement in human performance, occurring from the 1st-to-2nd learning trial, was also present in the optimal observer, and, thus reflects a property inherent to the visual task and not a property particular to the human perceptual learning mechanism. One notable source of human inefficiency is that, unlike the ideal observer, human learning relies more heavily on previous decisions than on the provided feedback, resulting in no human learning on trials following a previous incorrect localization decision. Finally, the proposed theory and paradigm provide a flexible framework for future studies to evaluate the optimality of human learning of other visual cues and/or sensory modalities.

Non-NASA Center↗

DOE OSTI2025

High-throughput spin-bath characterization of spin defects in semiconductors

Detailed knowledge of the local environments of spin defects in semiconductors, such as nitrogenvacancy (NV) centers in diamond or divacancies in silicon carbide, is crucial for optimizing control and entanglement protocols in quantum sensing and information applications. However, at present a direct experimental characterization of individual defect environments is not scalable, as conventional spin-bath measurements are time consuming and difficult to automate. Achieving high-throughput characterization requires short experiments to probe the spin bath. However, with fewer and noisier measurements, the inverse problem of recovering spin-bath properties from measured data becomes ill posed, with multiple spin baths having a high likelihood of yielding the same data. In this work, we present a set of computational tools to resolve the ill-posed inverse problem of recovering the atomic positions and hyperfine couplings of random nuclei surrounding spin defects from sparse, noisy experimental coherence data, which can be obtained in hours. Here, we use a trans-dimensional Bayesian approach that incorporates ab initio data to yield full posterior distributions over nuclear spin environments, enabling robust recovery from limited data. We also provide practical tools and guidelines to determine the limits of detectability for hyperfine couplings under specific dynamical decoupling sequences and sampling conditions. In addition, we demonstrate how the tools developed here, in combination with ab initio simulations of spin baths, can guide the design of efficient experimental protocols for application-specific high-throughput screening. To showcase the utility of our approach, we apply it to design fast dynamical decoupling experiments to characterize the spin baths often individual NV centers in diamond. While the primary focus is on accelerating spin-bath characterization of spin defects, this Bayesian approach also lays the foundation for digital-twin studies of spin defects, where a virtual model of the spin-defect system evolves in real time with ongoing experimental measurements. Together, the set of tools we designed and applied paves the way for scalable deployment of spin defects in semiconductors for quantum sensing and information applications.

Bayesian methods↗