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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

PROVABGS: The Probabilistic Stellar Mass Function of the BGS One-percent Survey

We present the probabilistic stellar mass function (pSMF) of galaxies in the DESI Bright Galaxy Survey (BGS), observed during the One-percent Survey. The One-percent Survey was one of DESI's survey validation programs conducted from 2021 April to May, before the start of the main survey. It used the same target selection and similar observing strategy as the main survey and successfully observed the spectra and redshifts of 143,017 galaxies in the r < 19.5 magnitude-limited BGS Bright sample and 95,499 galaxies in the fainter surface-brightness- and color-selected BGS Faint sample over z < 0.6. We derive pSMFs from posteriors of stellar mass, M*, inferred from DESI photometry and spectroscopy using the Hahn et al. PRObabilistic Value-Added BGS (PROVABGS) Bayesian spectral energy distribution modeling framework. We use a hierarchical population inference framework that statistically and rigorously propagates the M* uncertainties. Furthermore, we include correction weights that account for the selection effects and incompleteness of the BGS observations. We present the redshift evolution of the pSMF in BGS, as well as the pSMFs of star-forming and quiescent galaxies classified using average specific star formation rates from PROVABGS. Overall, the pSMFs show good agreement with previous stellar mass function measurements in the literature. Our pSMFs showcase the potential and statistical power of BGS, which in its main survey will observe >100 × more galaxies. Moreover, we present the statistical framework for subsequent population statistics measurements using BGS, which will characterize the global galaxy population and scaling relations at low redshifts with unprecedented precision.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

From Images to Dark Matter: End-to-end Inference of Substructure from Hundreds of Strong Gravitational Lenses

Abstract Constraining the distribution of small-scale structure in our universe allows us to probe alternatives to the cold dark matter paradigm. Strong gravitational lensing offers a unique window into small dark matter halos (<10 10 M ⊙ ) because these halos impart a gravitational lensing signal even if they do not host luminous galaxies. We create large data sets of strong lensing images with realistic low-mass halos, Hubble Space Telescope (HST) observational effects, and galaxy light from HST’s COSMOS field. Using a simulation-based inference pipeline, we train a neural posterior estimator of the subhalo mass function (SHMF) and place constraints on populations of lenses generated using a separate set of galaxy sources. We find that by combining our network with a hierarchical inference framework, we can both reliably infer the SHMF across a variety of configurations and scale efficiently to populations with hundreds of lenses. By conducting precise inference on large and complex simulated data sets, our method lays a foundation for extracting dark matter constraints from the next generation of wide-field optical imaging surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Map-based cosmology inference with lognormal cosmic shear maps

ABSTRACT Most cosmic shear analyses to date have relied on summary statistics (e.g. ξ+ and ξ−). These types of analyses are necessarily suboptimal, as the use of summary statistics is lossy. In this paper, we forward-model the convergence field of the Universe as a lognormal random field conditioned on the observed shear data. This new map-based inference framework enables us to recover the joint posterior of the cosmological parameters and the convergence field of the Universe. Our analysis properly accounts for the covariance in the mass maps across tomographic bins, which significantly improves the fidelity of the maps relative to single-bin reconstructions. We verify that applying our inference pipeline to Gaussian random fields recovers posteriors that are in excellent agreement with their analytical counterparts. At the resolution of our maps – and to the extent that the convergence field can be described by the lognormal model – our map posteriors allow us to reconstruct all summary statistics (including non-Gaussian statistics). We forecast that a map-based inference analysis of LSST-Y10 data can improve cosmological constraints in the σ8–Ωm plane by $\approx\!{30}{{\ \rm per\ cent}}$ relative to the currently standard cosmic shear analysis. This improvement happens almost entirely along the $S_8=\sigma _8\Omega _{\rm m}^{1/2}$ directions, meaning map-based inference fails to significantly improve constraints on S8.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Simultaneous inference of equation of state parameters and unknown data errors with uncertainty quantification via hierarchical Bayesian posterior maximization

Equations of state (EOSs) are a key component in running hydrodynamic simulations as they relate the thermodynamic states for the material. The Davis reactants EOS is commonly used for modeling high explosives (HEs), and the EOS model parameters are calibrated using material specific data. The calibrations are often performed with uncertainty quantification via Bayesian inference to account for uncertainty in the data and generate ensembles of likely parameters. However, there are relatively few HE data sets to use for calibration and many are historical and lack error information. In this work, we simultaneously calibrate the Davis reactants EOS model parameters and unknown data error terms for the high explosive PBX 9501. To quantify the uncertainty in the models and the data, we use a Bayesian framework for the calibration and compute the hierarchical Bayesian posterior distribution with both a posteriori maximization approach and Markov Chain Monte Carlo. In general, we find that, given our assumptions, the two approaches result in similar calibrated parameters, posterior covariance matrices, and insights about the parameters but that the posterior maximization requires far less computational resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Using Machine Learning to Generate a GISS ModelE Calibrated Physics Ensemble (CPE)

A neural network (NN) surrogate of the NASA GISS ModelE atmosphere (version E3) is trained on a perturbed parameter ensemble (PPE) spanning 45 physics parameters and 36 outputs. The NN is leveraged in a Markov Chain Monte Carlo (MCMC) Bayesian parameter inference framework to generate a second posterior constrained ensemble coined a “calibrated physics ensemble,” or CPE. The CPE members are characterized by diverse parameter combinations and are, by definition, close to top-of-atmosphere radiative balance, and must broadly agree with numerous hydrologic, energy cycle and radiative forcing metrics simultaneously. Global observations of numerous cloud, environment, and radiation properties (provided by global satellite products) are crucial for CPE generation. The inference framework explicitly accounts for discrepancies (or biases) in satellite products during CPE generation. We demonstrate that product discrepancies strongly impact calibration of important model parameter settings (e.g., convective plume entrainment rates; fall speed for cloud ice). Structural improvements new to E3 are retained across CPE members (e.g., stratocumulus simulation). Notably, the framework improved the simulation of shallow cumulus and Amazon rainfall while not degrading radiation fields, an upgrade that neither default parameters nor Latin Hypercube parameter searching achieved. Analyses of the initial PPE suggested several parameters were unimportant for output variation. However, many “unimportant” parameters were needed for CPE generation, a result that brings to the forefront how parameter importance should be determined in PPEs. From the CPE, two diverse 45-dimensional parameter configurations are retained to generate radiatively-balanced, auto-tuned atmospheres that were used in two E3 submissions to CMIP6.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Nonparametric Inference for the Reproductive Rate in Generalized Compartmental Models

We develop a tractable nonparametric model for the time-varying reproductive rate of infectious diseases that combines the structure of a deterministic compartmental model and a stochastic model for incidence data. We use Bayesian inference to estimate, with uncertainty, the reproductive rate of the Coronavirus 2019 outbreak in the U.S. states of California, Florida, Michigan, New Mexico, New York, and Texas from January 2020 to March 2022. Employing the inferred reproductive rates, we estimate the posterior distribution of the time-varying reproduction numbers for each state. Compering the time-varying reproduction numbers across the states, we identify some epidemic waves, potentially driven from changes in human behavior and virus mutations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Development of a Weibull posterior distribution by combining a Weibull prior with an actual failure distribution using Bayesian inference

A Bayesian inference process for system logistical planning is presented which provides a method for incorporating actual failures with prediction data for an ongoing and improving reliability estimates. The process uses the Weibull distribution, and provides a means for examining and updating logistical and maintenance support needs.

Giuntini, Michael E.↗
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 OSTI2022

Measuring the thermal and ionization state of the low- z IGM using likelihood free inference

ABSTRACT We present a new approach to measure the power-law temperature density relationship $T=T_0 (\rho/ \bar{\rho })^{\gamma -1}$ and the UV background photoionization rate $\Gamma _{{{{\rm H\, {\small I}}}}{}}$ of the intergalactic medium (IGM) based on the Voigt profile decomposition of the Ly α forest into a set of discrete absorption lines with Doppler parameter b and the neutral hydrogen column density $N_{\rm H\, {\small I}}$. Previous work demonstrated that the shape of the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution is sensitive to the IGM thermal parameters T0 and γ, whereas our new inference algorithm also takes into account the normalization of the distribution, i.e. the line-density dN/dz, and we demonstrate that precise constraints can also be obtained on $\Gamma _{{{{\rm H\, {\small I}}}}{}}$. We use density-estimation likelihood-free inference (DELFI) to emulate the dependence of the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution on IGM parameters trained on an ensemble of 624 nyx hydrodynamical simulations at z = 0.1, which we combine with a Gaussian process emulator of the normalization. To demonstrate the efficacy of this approach, we generate hundreds of realizations of realistic mock HST/COS data sets, each comprising 34 quasar sightlines, and forward model the noise and resolution to match the real data. We use this large ensemble of mocks to extensively test our inference and empirically demonstrate that our posterior distributions are robust. Our analysis shows that by applying our new approach to existing Ly α forest spectra at z ≃ 0.1, one can measure the thermal and ionization state of the IGM with very high precision ($\sigma _{\log T_0} \sim 0.08$ dex, σγ ∼ 0.06, and $\sigma _{\log \Gamma _{{{{\rm H\, {\small I}}}}{}}} \sim 0.07$ dex).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Robust Statistical Approach for Determination of Graphite Nitridation Using Bayesian Model Comparison

A better estimation of surface reaction efficiency of semiconductor-grade graphite with atomic nitrogen, as well as the calibration error are calculated using Bayesian updating based on experimental data. Compared with a conventional deterministic model, the stochastic model approach is a powerful tool in the sense that the model is capable of taking into account underlying error correlations among the data quantities. In this paper, we investigate four different stochastic models (called “stochastic system model classes” herein) corresponding to different descriptions of modeling and measurement error structures, given one deterministic physical model. These stochastic system model classes differ in the covariance matrix structure that is used in the uncertainty model to represent uncertainties associated with the physical model and experimental measurements. For each model class, Bayesian inference is used to estimate the posterior probabilities of the physical model parameters as well as of the stochastic model parameters. Model comparison and selection are then applied based on two measures including Bayesian evidence and Bayesian information criterion, as well as the deviance information criterion. Both measures suggest the stochastic model class, which considers that a correlation between errors in two data quantities among different data points is the most plausible. With the stochastic model class, the range of uncertainty in surface reaction efficiency is estimated to be about two orders of magnitude at [Formula: see text].

Engineering↗
DOE OSTI2020

The Distant, Galaxy Cluster Environment of the Short GRB 161104A at $z\sim 0.8$ and a Comparison to the Short GRB Host Population

We present optical observations of the Swift short-duration gamma-ray burst (GRB) GRB 161104A and its host galaxy at z = 0.793 ± 0.003. We model the multiband photometry and spectroscopy with the stellar population inference code Prospector and explore the posterior using nested sampling. We find a mass-weighted age of $t_m = 2.12^{+0.23}_{-0.21}$ Gyr, stellar mass of log(M/M ⊙ ), metallicity of log(Z/Z ⊙ ), dust extinction of $A_V = 0.08^{+0.08}_{-0.05}$, and low star formation rate of 9.9 × 10 -2 M ⊙ yr -1 . These properties, along with a prominent 4000 Å break and optical absorption lines, classify this host as an early-type, quiescent galaxy. Using Dark Energy Survey galaxy catalogs, we demonstrate that the host of GRB 161104A resides on the outskirts of a galaxy cluster at z ≈ 0.8, situated ≈1 Mpc from the likely brightest cluster galaxy. We also present new modeling for 20 additional short GRB hosts (≈33% of which are early-type galaxies), finding population medians of and $t_m = 1.07^{+1.98}_{-0.67}$ Gyr (68% confidence). We further find that the host of GRB 161104A is more distant, less massive, and younger than the four other short GRB hosts known to be associated with galaxy clusters. Cluster short GRBs have faint afterglows, in the lower ≈11% (≈30%) of observed X-ray (optical) luminosities. We place a lower limit on the fraction of short GRBs in galaxy clusters versus those in the field of ≈5%–13%, consistent with the fraction of stellar mass of ≈10%–20% in galaxy clusters at redshifts 0.1 ≤ z ≤ 0.8. Future studies that take advantage of wider-field and deeper cluster surveys are needed to understand the true rate of short GRBs in clusters and their effect on heavy-element enrichment in the intracluster medium.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Systems and methods for fast detection of elephant flows in network traffic

In a system for efficiently detecting large/elephant flows in a network, the rate at which the received packets are sampled is adjusted according to a top flow detection likelihood computed for a cache of flows identified in the arriving network traffic. After observing packets sampled from the network, Dirichlet-Categorical inference is employed to calculate a posterior distribution that captures uncertainty about the sizes of each flow, yielding a top flow detection likelihood. The posterior distribution is used to find the most likely subset of elephant flows. The technique rapidly converges to the optimal sampling rate at a speed O(1/n), where n is the number of packet samples received, and the only hyperparameter required is the targeted detection likelihood.

Gudibanda, Aditya↗
DOE OSTI2025

Galaxy cluster matter profiles - I. Self-similarity, mass calibration, and observable-mass relation validation employing cluster mass posteriors

We present a study of the weak lensing inferred matter profiles ΔΣ(R) of 698 South Pole Telescope (SPT) thermal Sunyaev-Zel’dovich effect (tSZE) selected and MCMF optically confirmed galaxy clusters in the redshift range 0.25 < z < 0.94 that have associated weak gravitational lensing shear profiles from the Dark Energy Survey (DES). Rescaling these profiles to account for the mass dependent size and the redshift dependent density produces average rescaled matter profiles ΔΣ(R/R200c)/(ρcritR200c) with a lower dispersion than the unscaled ΔΣ(R) versions, indicating a significant degree of self-similarity. Galaxy clusters from hydrodynamical simulations also exhibit matter profiles that suggest a high degree of self-similarity, with RMS variation among the average rescaled matter profiles with redshift and mass falling by a factor of approximately six and 23, respectively, compared to the unscaled average matter profiles. We employed this regularity in a new Bayesian method for weak lensing mass calibration that employs the so-called cluster mass posterior P(M200|ζ̂, λ̂, z), which describes the individual cluster masses given their tSZE (ζ̂) and optical (λ̂, z) observables. This method enables simultaneous constraints on richness λ-mass and tSZE detection significance ζ-mass relations using average rescaled cluster matter profiles. We validated the method using realistic mock datasets and present observable-mass relation constraints for the SPT×DES sample, where we constrained the amplitude, mass trend, redshift trend, and intrinsic scatter. Our observable-mass relation results are in agreement with the mass calibration derived from the recent cosmological analysis of the SPT×DES data based on a cluster-by-cluster lensing calibration. Our new mass calibration technique offers a higher efficiency when compared to the single cluster calibration technique. We present new validation tests of the observable-mass relation that indicate the underlying power-law form and scatter are adequate to describe the real cluster sample but that also suggest a redshift variation in the intrinsic scatter of the λ-mass relation may offer a better description. In addition, the average rescaled matter profiles offer high signal-to-noise ratio (S/N) constraints on the shape of real cluster matter profiles, which are in good agreement with available hydrodynamical ΛCDM simulations. This high S/N profile contains information about baryon feedback, the collisional nature of dark matter, and potential deviations from general relativity.Key words: gravitational lensing: weak / galaxies: clusters: general / large-scale structure of Universe

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Bayesian inference of Stochastic reaction networks using Multifidelity Sequential Tempered Markov Chain Monte Carlo

Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells.These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not directly measurable and must be inferred from experimental data. Bayesian inference provides a rigorous probabilistic frame-work for identifying these parameters by finding a posterior parameter distribution that captures their uncertainty.Traditional computational methods for solving inference problems such as Markov Chain Monte Carlo methods based on classical Metropolis-Hastings algorithm involve numerous serial evaluations of the likelihood function, which in turn requires expensive forward solutions of the chemical master equation (CME). We propose an alternate approach based on a multifidelity extension of the Sequential Tempered Markov Chain Monte Carlo (ST-MCMC) sampler. This algorithm is built upon Sequential Monte Carlo and solves the Bayesian inference problem by decomposing it into a sequence of efficiently solved subproblems that gradually increase both model fidelity and the influence of the observed data. We reformulate the finite state projection (FSP) algorithm, a well-known method for solving the CME, to produce a hierarchy of surrogate master equations to be used in this multifidelity scheme. To determine the appropriate fidelity, we introduce a novel information-theoretic criteria that seeks to extract the most information about the ultimate Bayesian posterior from each model in the hierarchy without inducing significant bias. This novel sampling scheme is tested with high performance computing resources using biologically relevant problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

The DESI PRObabilistic Value-added Bright Galaxy Survey (PROVABGS) Mock Challenge

The PRObabilistic Value-added Bright Galaxy Survey (PROVABGS) catalog will provide measurements of galaxy properties, such as stellar mass ($M*$), star formation rate (SFR), stellar metallicity (Z), and stellar age ($t_{age}$), for >10 million galaxies of the Dark Energy Spectroscopic Instrument (DESI) Bright Galaxy Survey. Full posterior distributions of the galaxy properties will be inferred using state-of-the-art Bayesian spectral energy distribution (SED) modeling of DESI spectroscopy and Legacy Surveys photometry. In this work, we present the SED model, the neural emulator for the model, and the Bayesian inference framework of PROVABGS. Furthermore, we apply the PROVABGS SED modeling on realistic synthetic DESI spectra and photometry, constructed using the L-Galaxies semi-analytic model. We compare the inferred galaxy properties to the true values of the simulation using a hierarchical Bayesian framework to quantify accuracy and precision. Overall, we accurately infer the true $M*$, SFR, Z, and $t_{age}$ of the simulated galaxies. However, the priors on galaxy properties induced by the SED model have a significant impact on the posteriors, which we characterize in detail. This work also demonstrates that a joint analysis of spectra and photometry significantly improves the constraints on galaxy properties over photometry alone and is necessary to mitigate the impact of the priors. With the methodology presented and validated in this work, PROVABGS will maximize information extracted from DESI observations and extend current galaxy studies to new regimes and unlock cutting-edge probabilistic analyses. https://github.com/changhoonhahn/provabgs/

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

How to Obtain the Redshift Distribution from Probabilistic Redshift Estimates

Abstract A reliable estimate of the redshift distribution n ( z ) is crucial for using weak gravitational lensing and large-scale structures of galaxy catalogs to study cosmology. Spectroscopic redshifts for the dim and numerous galaxies of next-generation weak-lensing surveys are expected to be unavailable, making photometric redshift (photo- z ) probability density functions (PDFs) the next best alternative for comprehensively encapsulating the nontrivial systematics affecting photo- z point estimation. The established stacked estimator of n ( z ) avoids reducing photo- z PDFs to point estimates but yields a systematically biased estimate of n ( z ) that worsens with a decreasing signal-to-noise ratio, the very regime where photo- z PDFs are most necessary. We introduce Cosmological Hierarchical Inference with Probabilistic Photometric Redshifts ( CHIPPR ), a statistically rigorous probabilistic graphical model of redshift-dependent photometry that correctly propagates the redshift uncertainty information beyond the best-fit estimator of n ( z ) produced by traditional procedures and is provably the only self-consistent way to recover n ( z ) from photo- z PDFs. We present the chippr prototype code, noting that the mathematically justifiable approach incurs computational cost. The CHIPPR approach is applicable to any one-point statistic of any random variable, provided the prior probability density used to produce the posteriors is explicitly known; if the prior is implicit, as may be the case for popular photo- z techniques, then the resulting posterior PDFs cannot be used for scientific inference. We therefore recommend that the photo- z community focus on developing methodologies that enable the recovery of photo- z likelihoods with support over all redshifts, either directly or via a known prior probability density.

79 ASTRONOMY AND ASTROPHYSICS↗
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 OSTI2021

B-PINNs: Bayesian Physics-informal Neural Networks for Forward and Inverse PDE Problems with Noisy Data

We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward and inverse nonlinear problems described by partial differential equations (PDEs) and noisy data. In this Bayesian framework, the Bayesian neural network (BNN) combined with a PINN for PDEs serves as the prior while the Hamiltonian Monte Carlo (HMC) or the variational inference (VI) could serve as an estimator of the posterior. B-PINNs make use of both physical laws and scattered noisy measurements to provide predictions and quantify the aleatoric uncertainty arising from the noisy data in the Bayesian framework. Compared with PINNs, in addition to uncertainty quantification, B-PINNs obtain more accurate predictions in scenarios with large noise due to their capability of avoiding overfitting. We conduct a systematic comparison between the two different approaches for the B-PINNs posterior estimation (i.e., HMC or VI), along with dropout used for quantifying uncertainty in deep neural networks. Our experiments show that HMC is more suitable than VI with mean field Gaussian approximation for the B-PINNs posterior estimation, while dropout employed in PINNs can hardly provide accurate predictions with reasonable uncertainty. Finally, we replace the BNN in the prior with a truncated Karhunen-Loève (KL) expansion combined with HMC or a deep normalizing flow (DNF) model as posterior estimators. The KL is as accurate as BNN and much faster but this framework cannot be easily extended to high-dimensional problems unlike the BNN based framework.

Non linear PDEs, Noisy data, Bysian physics inform↗