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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

DAmodel: hierarchical Bayesian modelling of DA white dwarfs for spectrophotometric calibration

We use hierarchical Bayesian modelling to calibrate a network of 32 all-sky faint DA white dwarf (DA WD) spectrophotometric standards (⁠16.5 < V , 19.5⁠) alongside three CALSPEC standards, from 912 Å to 32 μm. The framework is the first of its kind to jointly infer photometric zero points and WD parameters (surface gravity log g⁠, effective temperature T eff ⁠, extinction A V ⁠, dust relation parameter R V ) by simultaneously modelling both photometric and spectroscopic data. We model panchromatic Hubble Space Telescope Wide Field Camera 3 (HST/WFC3) UVIS and IR photometry, HST/STIS UV spectroscopy, and ground-based optical spectroscopy to sub-per cent precision. Photometric residuals for the sample are the lowest yet yielding < 0.004 mag RMS on average from the UV to the NIR, achieved by jointly inferring time-dependent changes in system sensitivity and WFC3/IR count-rate nonlinearity. Our GPU-accelerated implementation enables efficient sampling via Hamiltonian Monte Carlo, critical for exploring the high-dimensional posterior space. The hierarchical nature of the model enables population analysis of intrinsic WD and dust parameters. Inferred spectral energy distributions from this model will be essential for calibrating the James Webb Space Telescope as well as next-generation surveys, including Vera Rubin Observatory’s Legacy Survey of Space and Time and the Nancy Grace Roman Space Telescope.

methods: statistical↗
DOE OSTI2025

Hierarchical Bayesian Modeling for Cosmology: Can NPE reliably replace MCMC?

Hierarchical neural posterior estimation has its place Hierarchical Bayesian Modeling (HBM) combined with MCMC algorithms has been shown to provide more robust and accurate inference for real-world phenomena in which nature takes a nested form. However, MCMC-based inference can be computationally expensive, and its performance often suffers for complex posterior geometries. These costs are especially pertinent for HBM. Studies have recently demonstrated the potential for a flexible, expressive, and amortized hierarchical neural posterior estimator (HNPE) built on Normalizing Flows. These studies have mostly been performed on simple datasets, or they focus on a single parameter from each level of the hierarchy. A systematic study analyzing how both hierarchical methods compare for more complex and realistic datasets is necessary before applying HNPE for scientific measurements. Here, we re-explore the theory behind HNPE and conduct comparative numerical experiments of HNPE and MCMC-based HBM methods on real and synthetic data, including strong gravitational lensing simulations. In particular, we use a suite of diagnostics to show trade-offs in terms of accuracy, precision, time to train or sample, reproducibility, and the need for expert domain knowledge. Especially for higher dimensional and complex posteriors, HNPE is expected to drastically improve on time for inference, accuracy, and precision with an upfront training time cost.

Hur, Rachel [Chicago U.] (ORCID:000900089890445X)↗
DOE OSTI2024

Hierarchical Bayesian modeling for Inverse Uncertainty Quantification of system thermal-hydraulics code using critical flow experimental data

The best estimate plus uncertainty methodology in nuclear system thermal-hydraulic studies necessitates a comprehensive understanding of uncertainties in system code predictions. The forward uncertainty quantification (UQ) process involves the propagation of input uncertainties through the computational models to obtain uncertainties in the outputs. To this end, achieving an accurate estimation of input uncertainties is important, which is the focus of inverse UQ (IUQ). Traditionally, research in Bayesian IUQ within the nuclear engineering domain has largely relied on single-level Bayesian inference. While being effective for relatively small datasets, this approach encounters limitations for cases with large datasets. The use of a single-level model may prove inefficient, as the resultant posterior distributions can significantly differ when distinct subsets of data are employed. To address this issue, we employ an hierarchical Bayesian model for IUQ. Furthermore, this approach involves organizing observations into different groups based on the test conditions, thereby accommodating varying calibration parameters across these distinct groups. In this study, we developed and implemented a hierarchical Bayesian IUQ method to consider the grouping effect of critical flow measurement data from various geometries. Comparing the outcomes of IUQ under different selections of test data using hierarchical Bayesian IUQ against those obtained from single-level Bayesian IUQ, the forward propagation of hierarchical Bayesian IUQ results demonstrates a notably improved agreement with the experimental data.

42 ENGINEERING↗
NASA NTRS2023

Territory and Population Attributes Affect Florida Scrub-Jay Fecundity in Fire Adapted Ecosystems

Fecundity, the number of young produced by a breeding pair during a breeding season, is a primary component in evolutionary and ecological theory and applications. Fecundity can be influenced by many environmental factors and requires long-term study due to the range of variation in ecosystem dynamics. Fecundity data often include a large proportion of zeros when many pairs fail to produce any young during a breeding season due to nest failure or when all young die independently after fledging. We conducted color banding and monthly censuses of Florida scrub-jays (Aphelocoma coerulescens) across 31 years, 15 populations, and 761 territories along central Florida’s Atlantic coast. We quantified how fecundity (juveniles/pair-year) was influenced by habitat quality, presence/absence of nonbreeders, population density, breeder experience, and rainfall, with a zero-inflated Bayesian hierarchical model including both a Bernoulli (e.g., brood success) and a Poisson (counts of young) submodel, and random effects for year, population, and territory. The results identified the importance of increasing “strong” quality habitat, which was a mid-successional state related to fire frequency and extent, because strong territories, and the proportion of strong territories in the overall population, influenced fecundity of breeding pairs. Populations subject to supplementary feeding also had greater fecundity. Territory size, population density, breeder experience, and rainfall surprisingly had no or small effects. Different mechanisms appeared to cause annual variation in fecundity, as estimates of random effects were not correlated between the success and count submodels. The increased fecundity for pairs with nonbreeders, compared to pairs without, identified empirical research needed to understand how the proportion of low-quality habitats influences population recovery and sustainability, because dispersal into low-quality habitats can drain nonbreeders from strong territories and decrease overall fecundity. We also describe how long term study resulted in reversals in our understanding because of complications involving habitat quality, sociobiology, and population density.

Long-term studies↗
DOE OSTI2022

Technical note: Modeling spatial fields of extreme precipitation – a hierarchical Bayesian approach

Abstract. We introduce a hierarchical Bayesian model for the spatial distribution of rainfall corresponding to an extreme event of a specified duration that could be used with regional hydrologic models to perform a regional hydrologic risk analysis. An extreme event is defined if any gaging site in the watershed experiences an annual maximum rainfall event and the spatial field of rainfall at all sites corresponding to that occurrence is modeled. Applications to data from New York City demonstrate the effectiveness of the model for providing spatial scenarios that could be used for simulating loadings into the urban drainage system. Insights as to the homogeneity in spatial rainfall and its implications for modeling are provided by considering partial pooling in the hierarchical Bayesian framework.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2012

Astrophysical Model Selection in Gravitational Wave Astronomy

Theoretical studies in gravitational wave astronomy have mostly focused on the information that can be extracted from individual detections, such as the mass of a binary system and its location in space. Here we consider how the information from multiple detections can be used to constrain astrophysical population models. This seemingly simple problem is made challenging by the high dimensionality and high degree of correlation in the parameter spaces that describe the signals, and by the complexity of the astrophysical models, which can also depend on a large number of parameters, some of which might not be directly constrained by the observations. We present a method for constraining population models using a hierarchical Bayesian modeling approach which simultaneously infers the source parameters and population model and provides the joint probability distributions for both. We illustrate this approach by considering the constraints that can be placed on population models for galactic white dwarf binaries using a future space-based gravitational wave detector. We find that a mission that is able to resolve approximately 5000 of the shortest period binaries will be able to constrain the population model parameters, including the chirp mass distribution and a characteristic galaxy disk radius to within a few percent. This compares favorably to existing bounds, where electromagnetic observations of stars in the galaxy constrain disk radii to within 20%.

hierarchical↗
NASA NTRS2008

Interpolating Fields of Carbon Monoxide Data Using a Hybrid Statistical-Physical Model

Atmospheric Carbon Monoxide (CO) is a pollutant gas of which the US congress has mandated regular monitoring, and satellite sensors can be used to retrieve regional concentrations of CO over several vertical layers. However, CO at cloudy locations cannot be observed and have to be estimated from the observed data set, resulting in an interpolation problem. The current state-of-the-art solution is to combine prior information, computed by a deterministic physical model, with observations. However, the deterministic model may introduce uncertainties that do not derive from the data. While sharing certain features with the physical model, this paper presents a Bayesian hierarchical model for interpolating CO on a 3-dimensional spatial grid, across time. To our knowledge such a model has not been considered before. The model is applied to a hypothetical air-quality monitoring scenario, and is compared to existing interpolation methods. The results provide motivation for the use of the statistical model for regional to local applications.

Arellano, A. A.↗
NASA NTRS2023

Survival of Juvenile Florida Scrub-Jays is Habitat Specific, Positively Correlated With Month and Negatively Correlated With Male Breeder Death

Juvenile survival in birds is difficult to estimate but this vital rate can be an important consideration for management decisions. We estimated juvenile survival of cooperatively breeding Florida Scrub-Jays (Aphelocoma coerulescens) in a landscape degraded by fire suppression and fragmentation using data from marked (n = 325) and unmarked juveniles (n = 1,306) with an integrated hierarchical Bayesian model. To assess the combined analyses, we also analyzed these datasets separately, with a Cormack-Jolly-Seber (CJS) model (marked) and young model (unmarked). Our data consisted of monthly censuses of territorial family groups from Florida Scrub-Jay populations in East Central Florida collected over a 22-yr period. Juvenile survival was estimated from July when young Florida Scrub-Jays begin developing independence to March when they become first year individuals and grouped according to the habitat quality class of their natal territory that were based on shrub height (with intermediate shrub heights being optimal and short and tall shrub heights being suboptimal) and the presence of sandy openings (the preferred open having many sandy openings; closed not having enough). Parameter estimates in the combined analysis were intermediate to the separate analyses. Notable differences among the separate analyses were that suboptimal habitat survival was lower in the unmarked analysis, the unmarked analysis showed a linear effect of time not seen in the marked analysis, and there was an effect of male breeder death in the marked but not unmarked analysis. The combined data analysis provided more inference than did either data set analyzed separately including juveniles in optimal-closed territories unexpectedly had higher survival than those in optimal-open, survival increased through time, and male breeder death had a negative effect on survival. This study suggests that optimal-closed habitat may play an important role in juvenile Florida Scrub-Jay survival perhaps by providing better cover from predators and warrants further investigation for management implications.

Florida Scrub-Jay↗
DOE OSTI2025

Hot Droughts and Forest Tree Dynamics in the Amazon - Statistical Models, Scripts, Data, and Outputs

This package contains data, outputs, equations, and R scripts for analyses for manuscript entitled "Hot droughts in the Amazon: A window to a future hypertropical climate" by J. Chambers et al., in particular it contains statistical models and analyses for the INPA BIONTE tree mortality study. The Models folder contains details for all statistical models in PDF files. The Scripts folder contains the R scripts for Bayesian Hierarchical Models (two text files) and SEMs (one text file) are separate and reasonably annotated. All data associated with these scripts are in the data folder. The Data folder contains two of the three CSV files used for the analyses and are called by the R scripts. Two of them are part of published datasets (`BIONTE_mortality-rates.csv` from Lima et al. 2024, DOI:10.15486/ngt/1898910 and `SPEI.csv` from Pastorello et al. 2023 DOI:10.15486/ngt/1958257) and also provided in this package for convenience (please see the corresponding datasets for usage and citation terms). The third dataset (`BIONTE_gapfilled_wd.csv`) contains sensitive information and can be obtained by contacting the manuscript lead author. The Outputs folder contains the two output files that provide extra information about the analyses. The file `figuresFeb2025d.pdf` contains all the figures from the manuscript - captions are in the manuscript. The file `ChambersMS.pdf` contains primary results from Bayesian statistical models, regression analyses, and validation steps applied to the tree mortality data from the INPA experiments. The document includes visual summaries, model diagnostics, and leave-one-out (LOO) validation results. A breakdown of file contents can be found in the README file that is part of this package.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Spatial Bayesian models project shifts in suitable habitat for Pacific Northwest tree species under climate change

Abstract We developed spatial Bayesian hierarchical models to assess potential climate change impacts on suitable habitat for five important tree species in the Pacific northwestern United States (California, Oregon, and Washington). Individual‐species models were fit with presence–absence data from forest inventory field plots and spatial relationships were specified through a conditional autoregressive model. This modeling approach allowed us to visualize uncertainty in response curves, map current and future prediction uncertainty, and provide interval estimates for change. Upward elevational or northward latitudinal shifts in climatically suitable habitat were projected for all species. Climate change impacts were the most damaging for noble fir ( Abies procera ), for which 79%–100% of the current range was projected to become climatically unsuitable by the 2080s. Although coastal Douglas‐fir ( Pseudotsuga menziesii var. menziesii ) has been projected by others to gain habitat in Canada, within our study area we projected a net loss of climatically suitable habitat (ca. 8000–31,400 km 2 ) under three of four future climate scenarios. A net loss in habitat was also projected for Oregon white oak ( Quercus garryana ) under three of four scenarios, with 40%–60% of the current range becoming unsuitable. Although there was no net loss of habitat for forest land blue oak under any scenario, other factors like competition may inhibit blue oak ( Quercus douglasii ) and white oak from occupying areas projected to increase in climatic suitability. Additionally, between 13% and 32% of blue oak's current range was projected to become unsuitable; some of these areas aligned with dieback following the 2012–2015 California drought, which our data set predates. Unlike the other four species, we projected a 17%–25% increase in climatically suitable habitat for California black oak ( Quercus kelloggii ), although 1%–20% of the current range was still projected to become unsuitable. Our findings indicate that, although some species will face more pressure in tracking climatically suitable habitat than others, climate change will impact the location of suitable habitat for many species.

Kralicek, Karin↗
DOE OSTI2025

Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint

This paper analyzes hierarchical Bayesian inverse problems using techniques from highdimensional statistics. Furthermore, our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain non-asymptotic bounds on the reconstruction error attained by maximum a posteriori estimators. The new theory explains how hierarchical Bayesian models that exploit sparsity, group sparsity, and sparse representations of the unknown parameter can achieve accurate reconstructions in high-dimensional settings.

MAP estimation↗
DOE OSTI2026

Ecological connectivity and habitat loss shape patterns of genetic diversity in a threatened salamander

Context The maintenance of genetic diversity is essential for preserving adaptive potential in populations, yet it is increasingly threatened by landscape alteration. The field of landscape genetics offers a framework for assessing how patch-level landscape conditions, modeled at multiple scales, influence genetic diversity. Objectives We sought to assess how local environmental features and connectivity influence genetic diversity across 74 four-toed salamander (Hemidactylium scutatum) breeding wetlands in the southeastern United States. Methods Using next-generation sequencing data and hierarchical Bayesian models, we examined genome-wide heterozygosity in relation to local landscape features and ecological connectivity. We also assessed the scale of effect of landscape features and tested for temporal lag effects. Results Genetic diversity was lower in wetlands with higher levels of historic deforestation and lower connectivity. An interaction between deforestation and connectivity indicated that deforestation had stronger negative effects in isolated wetlands but weaker effects in well-connected wetlands. Accounting for scale of effect and temporal lags was critical for detecting these relationships. Conclusions Our analyses highlight the importance of assessing the spatial scale (scale of effect) and temporal lag of landscape features to detect key drivers of genetic diversity. In line with population genetic theory, our results indicate that the genetic consequences of habitat loss do not affect populations uniformly and are most severe in isolated populations where gene flow cannot buffer against loss of diversity. Altogether, we highlight the importance of considering the interaction of habitat loss and connectivity in conservation genetic management.

Hemidactylium scutatum↗
DOE OSTI2026

A Statistician’s Overview of Physics-Informed Neural Networks for Spatio-Temporal Data

The recent success of deep neural network models with physical constraints (so-called, Physics-Informed Neural Networks, PINNs) has led to renewed interest in the incorporation of mechanistic information in predictive models. Statisticians and others have long been interested in this problem, which has led to several practical and innovative solutions dating back decades. In this overview, we focus on the problem of data-driven prediction and inference of dynamic spatio-temporal processes that include mechanistic information, such as would be available from partial differential equations, with a strong focus on the quantification of uncertainty associated with data, process, and parameters. Here, we give a brief review of several paradigms and focus our attention on Bayesian implementations given they naturally accommodate uncertainty quantification. We then show that it is straight-forward to include the Bayesian PINN (B-PINN) within the Bayesian hierarchical model (BHM) framework that has long been considered for modeling dynamic spatio-temporal processes. Such a BHM-PINN is illustrated via a simulation study in which a latent nonlinear Burgers’ equation PDE governs the dynamics of Poisson distributed spatio-temporal data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Bayesian↗