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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Model Calibration with Markov Chain Monte Carlo Tutorial

The purpose of this tutorial is to demonstrate how to use Markov chain Monte Carlo (MCMC) to calibrate a model. By calibration, we mean the selection of model parameters (and, when relevant, structures). A common goal in model development and diagnostics is calibration, or the identification of model structures and parameters which are consistent with data. While models can be calibrated through hand-tuning parameters or minimizing simple error metrics such as root-mean-square-error (RMSE), these approaches can underrepresent the probabilistic nature of the data-generating process, as well as the potential for multiple model configurations to be consistent with the data. Probabilistic uncertainty quantification, which is the topic of this notebook, can address these concerns. This tutorial is presented as an appendix to the e-book: Addressing Uncertainty in MultiSector Dynamics Research.

Markov chain Monte Carlo↗
NASA NTRS2008

Five-Year Wilkinson Microwave Anisotropy Probe (WMAP1) Observations: Galactic Foreground Emission

We present a new estimate of foreground emission in the WMAP data, using a Markov chain Monte Carlo (MCMC) method. The new technique delivers maps of each foreground component for a variety of foreground models, error estimates of the uncertainty of each foreground component, and provides an overall goodness-of-fit measurement. The resulting foreground maps are in broad agreement with those from previous techniques used both within the collaboration and by other authors. We find that for WMAP data, a simple model with power-law synchrotron, free-free, and thermal dust components fits 90% of the sky with a reduced X(sup 2) (sub v) of 1.14. However, the model does not work well inside the Galactic plane. The addition of either synchrotron steepening or a modified spinning dust model improves the fit. This component may account for up to 14% of the total flux at Ka-band (33 GHz). We find no evidence for foreground contamination of the CMB temperature map in the 85% of the sky used for cosmological analysis.

Gold, B.↗
NASA NTRS2008

Black Hole Mergers as Probes of Structure Formation

Observations of gravitational waves from massive black hole (MBH) mergers can provide us with important clues about the era of structure formation in the early universe. Previous research in this field has been limited to calculating merger rates of MBHs using different models where many assumptions are made about the specific values of physical parameters of the mergers, resulting in merger rate estimates that span 5 to 6 orders of magnitude. We develop a semi-analytical, phenomenological model that includes plausible combinations of several physical parameters involved in the mergers. which we then turn around to determine how well LISA observations will be able to enhance our understanding of the universe during the critical z approximately equal to 5-30 structure formation era. We do this by generating synthetic LISA observable data (masses, redshifts, merger rates), which are then analyzed using a Markov Chain Monte Carlo (MCMC) method. This allows us to constrain the physical parameters of the mergers.

Alicea-Munoz, Emily↗
NASA NTRS2013

Estimating the Properties of Hard X-Ray Solar Flares by Constraining Model Parameters

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23.We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non- Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, Ec, a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that Ec lies below approximately 40 keV, and a 68% probability that it lies in the range 7-36 keV. Further, the low-energy cutoff is more likely to be in the range 25-35 keV than in any other 10 keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 +/- 4 keV with 68% probability.

X-rays↗
NASA NTRS2016

Integrating Chlorophyll fapar and Nadir Photochemical Reflectance Index from EO-1/Hyperion to Predict Cornfield Daily Gross Primary Production

The concept of light use efficiency (Epsilon) and the concept of fraction of photosynthetically active ration (PAR) absorbed for vegetation photosynthesis (PSN), i.e., fAPAR (sub PSN), have been widely utilized to estimate vegetation gross primary productivity (GPP). It has been demonstrated that the photochemical reflectance index (PRI) is empirically related to ε. An experimental US Department of Agriculture (USDA) cornfield in Maryland was selected as our study field. We explored the potential of integrating fAPAR(sub chl) (defined as the fraction of PAR absorbed by chlorophyll) and nadir PRI (PRI(sub nadir)) to predict cornfield daily GPP. We acquired nadir or near-nadir EO-1/Hyperion satellite images that covered the cornfield and took nadir in-situ field spectral measurements. Those data were used to derive the PRI(sub nadir) and fAPAR (sub chl). The fAPAR (sub chl) is retrieved with the advanced radiative transfer model PROSAIL2 and the Metropolis approach, a type of Markov Chain Monte Carlo (MCMC) estimation procedure. We define chlorophyll light use efficiency Epsilon (sub chl) as the ratio of vegetation GPP as measured by eddy covariance techniques to PAR absorbed by chlorophyll (Epsilon(sub chl) = GPP/APAR (sub chl). Daily Epsilon (sub chl) retrieved with the EO-1 Hyperion images was regressed with a linear equation of PRI (sub nadir) Epsilon (sub chl) = Alpha × PRI (sub nadir) + Beta). The satellite Epsilon(sub chl- PRI (sub nadir) linear relationship for the cornfield was implemented to develop an integrated daily GPP model [GPP = (Alpha × PRI(sub nadir) + Beta) × fAPAR (sub chl) × PAR], which was evaluated with fAPAR (sub chl) and PRI (sub nadir) retrieved from field measurements. Daily GPP estimated with this fAPAR (sub chl-) PRI (nadir) integration model was strongly correlated with the observed tower in-situ daily GPP (R(sup 2) = 0.93); with a root mean square error (RMSE) of 1.71 g C mol−(sup -1) PPFD and coefficient of variation (CV) of 16.57%. Both seasonal Epsilon (sub chl) and PRI (sub nadir) were strongly correlated with fAPAR (sub chl ) retrieved from field measurements, which indicates that chlorophyll content strongly affects seasonal epsilon (sub chl) and PRI (sub nadir). We demonstrate the potential capacity to monitor GPP with space-based visible through shortwave infrared (VSWIR) imaging spectrometers such as NASA's soon to be decommissioned EO- 1/Hyperion and the future Hyperspectral Infrared Imager (HyspIRI).

HyspIRI↗
NASA NTRS2016

A Computationally-Efficient Inverse Approach to Probabilistic Strain-Based Damage Diagnosis

This work presents a computationally-efficient inverse approach to probabilistic damage diagnosis. Given strain data at a limited number of measurement locations, Bayesian inference and Markov Chain Monte Carlo (MCMC) sampling are used to estimate probability distributions of the unknown location, size, and orientation of damage. Substantial computational speedup is obtained by replacing a three-dimensional finite element (FE) model with an efficient surrogate model. The approach is experimentally validated on cracked test specimens where full field strains are determined using digital image correlation (DIC). Access to full field DIC data allows for testing of different hypothetical sensor arrangements, facilitating the study of strain-based diagnosis effectiveness as the distance between damage and measurement locations increases. The ability of the framework to effectively perform both probabilistic damage localization and characterization in cracked plates is demonstrated and the impact of measurement location on uncertainty in the predictions is shown. Furthermore, the analysis time to produce these predictions is orders of magnitude less than a baseline Bayesian approach with the FE method by utilizing surrogate modeling and effective numerical sampling approaches.

Warner, James E.↗
NASA NTRS2019

Extratropical Large-Scale Traveling Weather Systems in the Southern Hemisphere on Mars

From late-autumn through early-spring, the middle- and high-latitudes of both hemispheres of Mars and its predominantly carbon-dioxide atmosphere support mean equator-to-pole thermal contrasts, and then, support a strong mean westerly polar vortex. Observations from orbiting spacecraft indicate that this intense mean baroclinicity-barotropicity supports large-scale eastward traveling weather systems (i.e., transient, traveling synoptic-period waves, on the order of the Rossby deformation scale). On Earth, extratropical weather disturbances arise from wind-shear instabilities, and these are critical components of the terrestrial global circulation. So it is the case for Mars. Large-scale traveling weather systems on Mars serve as agents in the transport of heat, momentum and scalar and tracer quantities (e.g., atmospheric dust, watervapor, ice clouds, chemical species, etc). Such weather systems interact with other large-scale atmospheric circulation components, namely, quasi-stationary (i.e., forced Rossby) modes; global thermal tidal modes; and then, upon large-/continental- geographical scales, upslope/ down-slope flows amongst high relief, low relief, impact basins, and volcanic rises, and more. The character of Mars' traveling extratropical weather disturbances in its southern hemisphere during late winter through early spring is investigated using a high-resolution Mars global climate model (i.e., Mars GCM), and one from the Agency's Mars Climate Modeling Center (MCMC) based at the NASA Ames Research Center. The climate model includes several complex atmospheric physical packages. With such physics modules, our global climate simulations present comparatively well with observations of the planet's current water cycle (Haberle et al.,2019). The climate model is "forced" with an annual dust cycle (i.e., nudged based on MGS/TES observations). Compared to the northern-hemisphere counterparts, the southern synoptic-period weather disturbances and accompanying frontal waves have smaller meridional and zonal scales, and are less intense. Influences of the zonally asymmetric (i.e., east-west varying) topography on southern large-scale weather are investigated, in addition to large-scale up-slope/down-slope flows and the diurnal cycle. A southern storm zone in late winter and early spring presents in the western hemisphere via orographic influences from the Tharsis highlands, and the Argyre and Hellas impact basins. Geographically localized transient-wave activity diagnostics are constructed that illuminate dynamical differences amongst the simulations and these are presented.

Hollingsworth, Jeffery L.↗
NASA NTRS2019

Machine Learning, Markov Chain Monte Carlo, and Optimal Algorithms to Characterize the AdvACT Kilopixel Transition-Edge Sensor Arrays

Next-generation focal planes comprising dozens of kilopixel transition-edge sensor (TES) arrays require new methods to rapidly screen candidate arrays, evaluate array non-idealities in the field, identify outlier devices for removal, and optimize the array performance in the field. We demonstrate robust methods to estimate TES parameters (critical temperatures and thermal conductivity parameters) and their uncertainties using a custom Markov Chain Monte Carlo (MCMC) algorithm. We also constrain systematic effects in estimating the TES parameters from non-isothermal current-voltage curves (IVs) at approximately a ~3% level. Additionally, for the first time, we have applied Machine Learning (ML) algorithms to tune detector arrays and optimize their performance.

Maria Salatino↗
NASA NTRS2021

TIC 168789840: A Sextuply Eclipsing Sextuple Star System

We report the discovery of a sextuply eclipsing sextuple star system from TESS data, TIC 168789840, also known as TYC 7037-89-1, the first known sextuple system consisting of three eclipsing binaries. The target was observed in Sectors 4 and 5 during Cycle 1, with light curves extracted from TESS Full Frame Image data. It was also previously observed by the WASP survey and ASAS-SN. The system consists of three gravitationally bound eclipsing binaries in a hierarchical structure of an inner quadruple system with an outer binary subsystem. Follow up observations from several different observatories were conducted as a means of determining additional parameters. The system was resolved by speckle interferometry with a 0 42 separation between the inner quadruple and outer binary, inferring an estimated outer period of ∼2 kyr. It was determined that the fainter of the two resolved components is an 8.217 day eclipsing binary, which orbits the inner quadruple that contains two eclipsing binaries with periods of 1.570 days and 1.306 days. Markov Chain Monte Carlo (MCMC) analysis of the stellar parameters has shown that the three binaries of TIC 168789840 are “triplets,” as each binary is quite similar to the others in terms of mass, radius, and Teff. As a consequence of its rare composition, structure, and orientation, this object can provide important new insight into the formation, dynamics, and evolution of multiple star systems. Future observations could reveal if the intermediate and outer orbital planes are all aligned with the planes of the three inner eclipsing binaries.

Brian P. Powell↗
NASA NTRS2021

Computational Inference of Vibratory System with Incomplete Modal Information Using Parallel, Interactive and Adaptive Markov Chains

Inverse analysis of vibratory system is an important subject in fault identification, model updating, and robust design and control. It is challenging subject because 1) the problem is oftentimes underdetermined while the measurements are limited and/or incomplete; 2) many combinations of parameters may yield results that are similar with respect to actual response measurements; and 3) uncertainties inevitably exist. The aim of this research is to leverage upon computational intelligence through statistical inference to facilitate an enhanced, probabilistic framework using incomplete modal response measurement. This new framework is built upon efficient inverse identification through optimization, whereas Bayesian inference is employed to account for the effect of uncertainties. To overcome the computational cost barrier, we adopt Markov chain Monte Carlo (MCMC) to characterize the target function/distribution. Instead of using single Markov chain in conventional Bayesian approach, we develop a new sampling theory with multiple parallel, interactive and adaptive Markov chains and incorporate it into Bayesian inference. This can harness the collective power of these Markov chains to realize the concurrent search of multiple local optima. The number of required Markov chains and their respective initial model parameters are automatically determined via Monte Carlo simulation-based sample pre-screening followed by K-means clustering analysis. These enhancements can effectively address the aforementioned challenges in finite element inverse analysis. The validity of this framework is systematically demonstrated through case studies.

K Zhou↗
NASA NTRS2024

TOI-3568 b: A Super-Neptune in the Sub-Jovian Desert

The sub-Jovian desert is a region in the mass–period and radius–period parameter space that typically encompasses short-period ranges between super-Earths and hot Jupiters, and exhibits an intrinsic dearth of planets. This scarcity is likely shaped by photo evaporation caused by the stellar irradiation received by giant planets that have migrated inward. We report the detection and characterization ofTOI-3568 b, a transiting super-Neptune with a mass of26.4±1.0M⊕, a radius of5.30±0.27R⊕, a bulk density of0.98±0.15g cm−3, and an orbital period of 4.417965 (5) d situated in the vicinity of the sub-Jovian desert. This planet orbiting a K dwarf star with solar metallicity was identified photometrically by the Transiting Exoplanet Survey Satellite (TESS). It was characterized as a planet by our high-precision radial-velocity (RV) monitoring program using MAROON-X at Gemini North, supplemented with additional observations from the SPICE large program with SPIRou at CFHT. We performed a Bayesian MCMC joint analysis of the TESSand ground-based photometry, and MAROON-X and SPIRou RVs, to measure the orbit, radius, and mass of the planet, as well as a detailed analysis of the high-resolution flux and polarimetric spectra to determine the physical parameters and elemental abundances of the host star. Our results reveal TOI-3568 b to be a hot super-Neptune rich in hydrogen and helium, with a core of heavier elements of between 10 and 25 M⊕in mass. We analyzed the photo evaporation status of TOI-3568 b and find that it experiences one of the highest extreme-ultraviolet (EUV) luminosities among planets with a mass of Mp<2MNep, yet it has an evaporation lifetime exceeding 5 Gyr. Positioned in the transition between two significant populations of exoplanets on the mass–period and energy diagrams, this planet presents an opportunity to test theories concerning the origin of the sub-Jovian desert.

stars: individual: TOI-3568↗
DOE OSTI2024

A Measurement of νe Appearance and νµ Disappearance Using 10 Years of Data from the NOvA Experiment

NOvA is a long baseline neutrino experiment with an 810 km baseline, using the NuMIbeam at Fermilab, and a functionally identical near and far detector operating at an angle14 mrad off axis from the beam. NOvA jointly measures muon neutrino (and antineutrino)disappearance and electron neutrino (and antineutrino) appearance to make a measurementof sin2θ23, δCP, and ∆m232, including its sign, the mass ordering.This dissertation reports a new measurement from NOvA, using 10 years of data, with a totalexposure of 26.6 ×1020 POT of neutrino beam and 12.5 ×1020 POT of antineutrino beam.This represents 95.6% more neutrino beam exposure since the last NOvA analysis. Aspects ofthe analysis are discussed in detail, including neutrino energy estimation, analysis systematicuncertainties, including the implementation of systematics new to the NOvA analysis, andthe Bayesian fit infrastructure using Markov Chain Monte Carlo (MCMC).The analysis yields the following credible intervals for the oscillation parameters assumingthe normal ordering: δCP = 0.930+0.210−0.290 π ∪0.150+0.150−0.110 π,∆m232 = 2.424+0.035−0.040 × 10−3eV2,and sin2θ23 = 0.55+0.02−0.06, with a 76% preference for normal ordering using a prior for sin2(2θ13)using Daya Bay’s measurement. If the Daya Bay sin2(2θ13) vs ∆m232 constraint is used as aprior instead, an 87% preference for normal ordering emerges.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

Probabilistic Inference of Low-Surface-Brightness Galaxy Morphological Parameters Using Simulation-Based Inference

Low-surface-brightness galaxies (LSBGs) are diffuse, often dark-matter-dominated systems whose faintness makes their structural parameters difficult to measure reliably in wide-field imaging surveys. Robust parameter inference, including uncertainty quantification, is important for population studies and for comparisons with models of galaxy formation, as future surveys are expected to produce increasingly large samples of diffuse galaxies. In practice, LSBG profile modeling is sensitive to sky- background errors, masking choices, contaminating background sources, and the computational cost of obtaining posterior-level uncertainties for large samples. Motivated by these questions, we develop a simulation-based inference (SBI) framework for estimating posterior distributions of LSBG morphological parameters from simulated galaxy images. Using PyImfit, we generate DES-like single-Sersic profile LSBG images with known position angle, ellipticity, Sersic index, effective surface brightness, and effective radius. We then train a normalizing-flow-based neural posterior estimator using the sbi package to infer these parameters from the simulated images. For isolated simulated galaxies, the SBI posterior recovers the true input parameters, produces posterior predictive residuals consistent with the assumed noise model, and shows good empirical calibration in a DES-motivated test regime. We also compare SBI with PyImfit-based MCMC inference and find broadly comparable posterior constraints, while SBI enables substantially faster posterior sampling after training. Finally, we test robustness to compact background contaminants. A model trained only on isolated galaxies produces undercovered posteriors on contaminated images, whereas training on simulations with variable contaminant positions and fluxes improves calibration across contaminated test sets. These results demonstrate the promise of SBI for scalable, uncertainty-aware LSBG morphology inference, while emphasizing that posterior reliability strongly depends on whether training simulations include relevant observational complications.

Batbayar, Bilguun [U. Chicago (main)]↗
DOE OSTI2025

Generalized fiducial inference on differentiable manifolds

We introduce a novel approach to inference on parameters that take values in a Riemannian manifold embedded in a Euclidean space. Parameter spaces of this form are ubiquitous across many fields, including chemistry, physics, computer graphics, and geology. Here, this new approach uses generalized fiducial inference (GFI) to obtain a posterior-like distribution on the manifold, without needing to know local parameterizations that map to the constrained space from an unconstrained Euclidean space. Using mathematical tools from Riemannian geometry, we construct a constrained generalized fiducial distribution (CGFD). A Bernstein-von Mises-type result for the CGFD, which provides intuition for how the desirable asymptotic qualities of the unconstrained generalized fiducial distribution are inherited by the CGFD, is provided. To illustrate the practical use of the CGFD, we provide a proof-of-concept example in the context of a linear logspline density estimation problem, and demonstrate that CGFD-based confidence sets exhibit desirable coverage properties via simulation. As an application, we fit a CGFD to COVID-19 case count data from North Carolina, USA.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Using PyBioNetFit to leverage qualitative and quantitative data in biological model parameterization and uncertainty quantification

Data generated in studies of cellular regulatory systems are often qualitative. For example, measurements of signaling readouts in the presence and absence of mutations may reveal a rank ordering of responses across conditions but not the precise extents of mutation-induced differences. Qualitative data are often ignored by mathematical modelers or are considered in an ad hoc manner, as in the study of Kocieniewski and Lipniacki (2013) [Phys Biol 10: 035006], which was focused on the roles of MEK isoforms in ERK activation. In this earlier study, model parameter values were tuned manually to obtain consistency with a combination of qualitative and quantitative data. This approach is not reproducible, nor does it provide insights into parametric or prediction uncertainties. Here, starting from the same data and the same ordinary differential equation (ODE) model structure, we generate formalized statements of qualitative observations, making these observations more reusable, and we improve the model parameterization procedure by applying a systematic and automated approach enabled by the software package PyBioNetFit. We also demonstrate uncertainty quantification (UQ), which was absent in the original study. Our results show that PyBioNetFit enables qualitative data to be leveraged, together with quantitative data, in parameterization of systems biology models and facilitates UQ. These capabilities are important for reliable estimation of model parameters and model analyses in studies of cellular regulatory systems and reproducibility.

59 BASIC BIOLOGICAL SCIENCES↗