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NASA NTRS2021

Atacama Cosmology Telescope measurements of a large sample of candidates from the Massive and Distant Clusters of WISE Survey: Sunyaev-Zeldovich effect confirmation of MaDCoWS candidates using ACT

Context. Galaxy clusters are an important tool for cosmology, and their detection and characterization are key goals for current and future surveys. Using data from the Wide-field Infrared Survey Explorer (WISE), the Massive and Distant Clusters of WISE Survey (MaDCoWS) located 2839 significant galaxy overdensities at redshifts 0.7 . z . 1.5, which included extensive follow-up imaging from the Spitzer Space Telescope to determine cluster richnesses. Concurrently, the Atacama Cosmology Telescope (ACT) has produced large area millimeter-wave maps in three frequency bands along with a large catalog of Sunyaev-Zeldovich (SZ)-selected clusters as part of its Data Release 5 (DR5). Aims. We aim to verify and characterize MaDCoWS clusters using measurements of, or limits on, their thermal SZ effect signatures. We also use these detections to establish the scaling relation between SZ mass and the MaDCoWS-defined richness. Methods. Using the maps and cluster catalog from DR5, we explore the scaling between SZ mass and cluster richness. We do this by comparing cataloged detections and extracting individual and stacked SZ signals from the MaDCoWS cluster locations. We use complementary radio survey data from the Very Large Array, submillimeter data from Herschel, and ACT 224 GHz data to assess the impact of contaminating sources on the SZ signals from both ACT and MaDCoWS clusters. We use a hierarchical Bayesian model to fit the mass-richness scaling relation, allowing for clusters to be drawn from two populations: one, a Gaussian centered on the mass-richness relation, and the other, a Gaussian centered on zero SZ signal. Results. We find that MaDCoWS clusters have submillimeter contamination that is consistent with a gray-body spectrum, while the ACT clusters are consistent with no submillimeter emission on average. Additionally, the intrinsic radio intensities of ACT clusters are lower than those of MaDCoWS clusters, even when the ACT clusters are restricted to the same redshift range as the MaDCoWS clusters. We find the best-fit ACT SZ mass versus MaDCoWS richness scaling relation has a slope of p1 = 1.84+0.15 −0.14, where the slope is defined as M ∝ λ p1 15 and λ15 is the richness. We also find that the ACT SZ signals for a significant fraction (∼57%) of the MaDCoWS sample can statistically be described as being drawn from a noise-like distribution, indicating that the candidates are possibly dominated by low-mass and unvirialized systems that are below the mass limit of the ACT sample. Further, we note that a large portion of the optically confirmed ACT clusters located in the same volume of the sky as MaDCoWS are not selected by MaDCoWS, indicating that the MaDCoWS sample is not complete with respect to SZ selection. Finally, we find that the radio loud fraction of MaDCoWS clusters increases with richness, while we find no evidence that the submillimeter emission of the MaDCoWS clusters evolves with richness. Conclusions. We conclude that the original MaDCoWS selection function is not well defined and, as such, reiterate the MaDCoWS collaboration’s recommendation that the sample is suited for probing cluster and galaxy evolution, but not cosmological analyses. We find a best-fit mass-richness relation slope that agrees with the published MaDCoWS preliminary results. Additionally, we find that while the approximate level of infill of the ACT and MaDCoWS cluster SZ signals (1–2%) is subdominant to other sources of uncertainty for current generation experiments, characterizing and removing this bias will be critical for next-generation experiments hoping to constrain cluster masses at the sub-percent level.

large↗

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↗

NASA NTRS1989

A Bayesian approach to reliability and confidence

The historical evolution of NASA's interest in quantitative measures of reliability assessment is outlined. The introduction of some quantitative methodologies into the Vehicle Reliability Branch of the Safety, Reliability and Quality Assurance (SR and QA) Division at Johnson Space Center (JSC) was noted along with the development of the Extended Orbiter Duration--Weakest Link study which will utilize quantitative tools for a Bayesian statistical analysis. Extending the earlier work of NASA sponsor, Richard Heydorn, researchers were able to produce a consistent Bayesian estimate for the reliability of a component and hence by a simple extension for a system of components in some cases where the rate of failure is not constant but varies over time. Mechanical systems in general have this property since the reliability usually decreases markedly as the parts degrade over time. While they have been able to reduce the Bayesian estimator to a simple closed form for a large class of such systems, the form for the most general case needs to be attacked by the computer. Once a table is generated for this form, researchers will have a numerical form for the general solution. With this, the corresponding probability statements about the reliability of a system can be made in the most general setting. Note that the utilization of uniform Bayesian priors represents a worst case scenario in the sense that as researchers incorporate more expert opinion into the model, they will be able to improve the strength of the probability calculations.

Barnes, Ron↗

NASA NTRS2008

Potential Use of a Bayesian Network for Discriminating Flash Type from Future GOES-R Geostationary Lightning Mapper (GLM) data

Continuous monitoring of the ratio of cloud flashes to ground flashes may provide a better understanding of thunderstorm dynamics, intensification, and evolution, and it may be useful in severe weather warning. The National Lighting Detection Network TM (NLDN) senses ground flashes with exceptional detection efficiency and accuracy over most of the continental United States. A proposed Geostationary Lightning Mapper (GLM) aboard the Geostationary Operational Environmental Satellite (GOES-R) will look at the western hemisphere, and among the lightning data products to be made available will be the fundamental optical flash parameters for both cloud and ground flashes: radiance, area, duration, number of optical groups, and number of optical events. Previous studies have demonstrated that the optical flash parameter statistics of ground and cloud lightning, which are observable from space, are significantly different. This study investigates a Bayesian network methodology for discriminating lightning flash type (ground or cloud) using the lightning optical data and ancillary GOES-R data. A Directed Acyclic Graph (DAG) is set up with lightning as a "root" and data observed by GLM as the "leaves." This allows for a direct calculation of the joint probability distribution function for the lighting type and radiance, area, etc. Initially, the conditional probabilities that will be required can be estimated from the Lightning Imaging Sensor (LIS) and the Optical Transient Detector (OTD) together with NLDN data. Directly manipulating the joint distribution will yield the conditional probability that a lightning flash is a ground flash given the evidence, which consists of the observed lightning optical data [and possibly cloud data retrieved from the GOES-R Advanced Baseline Imager (ABI) in a more mature Bayesian network configuration]. Later, actual GLM and NLDN data can be used to refine the estimates of the conditional probabilities used in the model; i.e., the Bayesian network is a learning network. Methods for efficient calculation of the conditional probabilities (e.g., an algorithm using junction trees), finding data conflicts, goodness of fit, and dealing with missing data will also be addressed.

Solakiewiz, Richard↗

DOE OSTI2026

Forest aboveground biomass estimation through integration of sentinel-2 and PALSAR-2 time series: assessing models trained on GEDI and field inventory benchmarks

Accurate and spatially explicit forest Aboveground Biomass (AGB) mapping through remote sensing is critical for quantifying terrestrial carbon stocks and informing effective forest management strategies. However, AGB estimation in dense forests with complex terrain remains challenging due to satellite sensor signal saturation problem (saturation issue occurs in high biomass forests), structural complexity, and limited ground truth for calibration. This study presents a novel framework that integrates multi-temporal Sentinel-2 optical imagery, ALOS PALSAR-2 Synthetic Aperture Radar (SAR) data, and topographic variables with explainable Machine Learning to map AGB across mountainous forests within subtropical and temperate oceanic climate zones of Mexico. We evaluate the effects of temporal granularity and sensor synergy by comparing multiple temporal inputs and sensor configurations (Sentinel-2, PALSAR-2, and their fusion), and assess model performance using two reference datasets: NASA GEDI LiDAR-derived biomass and Mexico’s National Forest and Soil Inventory (INFyS). Our results showed that models trained on INFyS consistently outperformed those trained on GEDI, highlighting limitations in GEDI’s reliability in biomass estimates within this study region. Furthermore, the integration of Sentinel-2 and PALSAR-2 provided improved predictions compared to single-sensor models, particularly when combined with temporally explicit yearly statistics. The best-performing model, which was trained on INFyS data, and considered both Sentinel-2 and PALSAR-2 yearly statistics, as well as topographic variables, achieved an R2 of 0.64, RMSE of 51.10 Mg/ha, and relative RMSE (rRMSE) of 58.69%. Explainable ML analysis identified Sentinel-2 spectral indices and topographic features as key predictors, while PALSAR-2 metrics provided complementary information, partially mitigating saturation effects in high-biomass areas. Specifically, integrating both sensors substantially improved AGB estimation in high biomass forest (≥200 Mg/ha), yielding 98% gains over optical-only model, with resulting estimates exceeding GEDI L4B by 29% and ESA-CCI-BIOMASS by 174%. Terrain-stratified analysis indicated close agreement with GEDI in low-slope areas, with increasing divergence as slope steepness increased, while estimates remained consistently higher than ESA-CCI-BIOMASS across all slope classes. The proposed approach advances multi-sensor fusion and temporal feature engineering for AGB mapping using open-access satellite datasets, providing a scalable and reproducible framework for annual biomass monitoring in topographically complex mountainous forests. The resulting 25 m resolution biomass product has the potential to provide spatially detailed information for forest monitoring and may support applications in carbon accounting and forest management.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2002

The footprints of visual attention in the Posner cueing paradigm revealed by classification images

In the Posner cueing paradigm, observers' performance in detecting a target is typically better in trials in which the target is present at the cued location than in trials in which the target appears at the uncued location. This effect can be explained in terms of a Bayesian observer where visual attention simply weights the information differently at the cued (attended) and uncued (unattended) locations without a change in the quality of processing at each location. Alternatively, it could also be explained in terms of visual attention changing the shape of the perceptual filter at the cued location. In this study, we use the classification image technique to compare the human perceptual filters at the cued and uncued locations in a contrast discrimination task. We did not find statistically significant differences between the shapes of the inferred perceptual filters across the two locations, nor did the observed differences account for the measured cueing effects in human observers. Instead, we found a difference in the magnitude of the classification images, supporting the idea that visual attention changes the weighting of information at the cued and uncued location, but does not change the quality of processing at each individual location.

Non-NASA Center↗

DOE OSTI2025

On Finding Black Holes in Photometric Microlensing Surveys

There are expected to be millions of isolated black holes in the galaxy resulting from the deaths of massive stars. Measuring the abundance and properties of this remnant population would shed light on the end stages of stellar evolution and the evolution paths of black hole systems. Detecting isolated black holes is currently only possible via gravitational microlensing, which has so far yielded one definitive detection. The difficulty in finding microlensing black holes lies in having to choose a small subset of events, based on characteristics of their light curves, to allocate expensive and scarce follow-up resources to confirm the identity of the lens. Current methods either rely on simple cuts in parameter space without using the full distribution information or are only effective on small subsets of events. In this paper, we present a new lens classification method. The classifier takes in posterior constraints on light-curve parameters and combines them with a Galactic simulation to estimate the lens class probability. This method is flexible and can be used with any set of microlensing light-curve parameters, making it applicable to large samples of events. We make this classification framework available via the popclass Python package. We apply the classifier to ~10,000 microlensing events from the Optical Gravitational Lensing Experiment survey and find 23 high-probability black hole candidates. Our classifier also suggests that the only known isolated black hole is an observational outlier, according to current Galactic models, and the allocation of astrometric follow-up on this event was a high-risk strategy.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Angular Distribution of Dimuons from Drell-Yan Production in p+Fe Interactions at 120 GeV Beam Energy

In the E906/SeaQuest Fermilab experiment, we report a measurement of the angular distributions by measuring the angular parameters $\lambda$, $\mu$, and $\nu$ of Drell-Yan dimuons produced using a 120 GeV proton beam incident on an iron target. The angular distribution in the naive Drell-Yan model does not show any $\cos2\phi$ dependency, where $\phi$ denotes the azimuthal angle of dimuons in the Collins-Soper frame. However, pion-induced Drell-Yan experiments, such as NA10 and E615, have observed a significant dependence on $\cos2\phi$. The Boer–Mulders function, a transverse momentum-dependent distribution function, represents the correlation between the transverse spin and the transverse momentum of the quark. A non-zero Boer-Mulders function or an improved higher-order Drell-Yan model considering QCD effects can produce a $\cos 2\phi$ modulation in the Drell-Yan angular distribution. To measure the angular distributions, we have used an event mixing method to construct the combin atorial background, which was then subtracted from the data to isolate the Drell-Yan signal. Following this, we corrected the detector, trigger, and reconstruction efficiencies using a doubly-iterative Bayesian Unfolding method. This iterative unfolding technique improves the response matrix based on the results of the previous unfolding step, ensuring robust convergence without exaggeration of uncertainties. The angular distributions of the dimuons were measured over the invariant mass range $5.0 < M_{\mu^+ \mu^-} < 8.0$ $GeV/c^2$, with dimuon transverse momentum $P_T < 2$ GeV/c and Feynman-x $-0.18 < x_F < 0.9$. The measured angular distributions are then compared with the QCD calculations for $p + \text{Fe}$ interactions, and proton-induced angular distribution measurements from other experiments. We have observed weak $\cos 2\phi$ modulations as a function of $P_T$. For $P_T > 1.0 \, \text{GeV}/c$, the predicted NNLO perturbative QCD value of $\nu$ is larger than what we have me asured at E906/SeaQuest. Moreover, we have not observed a strong dependence of $\nu$ on the kinematic variables, such as dimuon mass $M_{\mu^+ \mu^-}$ and Bjorken-$x$. The spin alignment of the virtual photon, $\lambda$, measured from the SeaQuest Drell-Yan $p+\text{Fe}$ data, is found to be strongly dependent on $P_T$, decreasing as $P_T$ increases. $\lambda$ also holds to the upper bound condition $\lambda < 1.0$ within the statistical uncertainty, showing a trend similar to that predicted by NNLO perturbative QCD. However, for $1.0 < P_T < 2.0 \, \text{GeV}/c$, the extracted $\lambda$ value from SeaQuest is smaller than that predicted by perturbative QCD at NNLO.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Validating sequential Monte Carlo for gravitational-wave inference

Nested sampling (NS) is the preferred stochastic sampling algorithm for gravitational-wave inference for compact binary coalescences. It can handle the complex nature of the gravitational-wave likelihood surface and provides an estimate of the Bayesian model evidence. However, there is another class of algorithms that meets the same requirements, but has not been used for gravitational-wave analyses: sequential Monte Carlo (SMC), an extension of importance sampling that maps samples from an initial density to a target density via a series of intermediate densities. In this work, we validate a type of SMC algorithm, called persistent sampling (PS), for gravitational-wave inference. We consider a range of different scenarios including binary black holes and binary neutron stars and real and simulated data and show that PS produces results that are consistent with NS whilst being, on average, 2 times more efficient and 2.74 times faster. This demonstrates that PS is a viable alternative to NS that should be considered for future gravitational-wave analyses.

black hole mergers↗

DOE OSTI2025

Analysis of streaked images of x-ray self-emission in laser-driven spherical implosions

Imaging of x-ray self-emission provides a powerful in situ measurement of the spatial and temporal evolution of high-energy-density plasmas. However, interpretation of these measurements requires detailed understanding of the data-generating process. This work presents a case study in the interpretation of x-ray self-emission data for the specific application of streaked one-dimensional slit imaging of spherical laser-driven implosions. A comprehensive generative model of the streaked slit-imaging diagnostic is developed including detailed treatments of the radiation transfer, photometrics, and photostatistics associated with the measurement. The model is used to generate realistic synthetic streaked images and to analyze experimental streaked images to extract important physical quantities of interest. An example analysis of streaked images from implosion experiments on the OMEGA laser is presented, where the model developed in this work is used to constrain the trajectory and peak velocity of the implosion using Bayesian inference.

Bayesian inference↗

DOE OSTI2026

pop-cosmos : redshifts and physical properties of KiDS-1000 galaxies

ABSTRACT Principled Bayesian inference of galaxy properties has not previously been performed for wide-area weak-lensing surveys with millions of sources. We address this gap by applying the pop-cosmos generative model to perform spectral energy distribution (SED) fitting for 4 million KiDS (Kilo-Degree Survey)-1000 galaxies. Calibrated on deep COSMOS2020 photometric data, pop-cosmos specifies a physically motivated prior over the galaxy population up to $z \simeq 6$ in stellar population synthesis (SPS) parameter space. Using the Speculator SPS emulator with GPU (graphics processing unit)-accelerated Markov Chain Monte Carlo sampling, we perform full posterior inference at 8.2 GPU seconds per galaxy, obtaining joint constraints on galaxy redshifts and physical properties. We validate photometric redshifts against $\sim \!185\,\!000$ KiDS galaxies cross-matched to Dark Energy Spectroscopic Instrument Data Release 1 spectroscopic samples, achieving low bias ($2\times 10^{-3}$), scatter ($\sigma _{\mathrm{MAD}}=0.03$), and outlier fraction (3.2 per cent) for the Bright Galaxy Survey, with comparable performance (bias $3\times 10^{-2}$, $\sigma _{\mathrm{MAD}}=0.05$, 1.0 per cent outliers) for luminous red galaxies (LRGs). Within the LRG sample, we identify massive, dusty, star-forming contaminants at $z \simeq 0.4$ satisfying standard colour selections for quenched populations. We infer trends in stellar mass, star formation, metallicity, and dust across five tomographic redshift bins consistent with established scaling relations. Using specific star formation rate constraints, we identify $\sim$7 per cent of KiDS-1000 galaxies as quenched, versus 37 per cent implied by conservative colour cuts. This enables the construction of weak-lensing samples defined by physical properties while mitigating intrinsic alignment systematics and preserving statistical power. Our analysis validates pop-cosmos out of sample, establishing it as a scalable approach for galaxy evolution and cosmological analyses with photometric surveys.

Halder, Anik [Institute of Astronomy and Kavli Ins↗

NASA NTRS2017

Detection of Vegetation Trends in Highly Variable Environments After Grazing Exclusion in Mongolia

Aims: Environmental variability (e.g. in precipitation) has a large effect on vegetation dynamics, and this often makes it difficult to assess the recovery of vegetation after a disturbance. In this study, we assessed vegetation recovery trends in response to grazing exclusion while considering for the annual environmental variability. Location: Two regions with highly variable precipitation: a steppe near Mandalgobi, in Mongolia's Central Gobi province, and a desert steppe near Bulgan, in Mongolia's South Gobi province. Methods: Changes in vegetation were observed along grazing gradients at the above two sites, and vegetation thresholds were identified. We established reference plots in pre-threshold areas along the grazing gradients. We removed the impact of livestock grazing at various locations along the grazing gradients by establishing exclosures, and investigated vegetation from 2005 to 2013. We developed a smoothed hierarchical model within a Bayesian framework, and examined the effect of grazing exclusion on vegetation, focusing especially on the extent of grass cover recovery. In addition, we compared soil nutrient conditions in the reference plots and inside and outside each exclosure along the grazing gradients. Results: Temporal trends in the cover of perennial grass in each plot inside and outside of the exclosures largely coincided, irrespective of grazing intensity, and exclosure had no effect (Bulgan) or a negative effect (Mandalgobi) on vegetation recovery. Soil nutrient content was not significantly affected by exclosure at a given distance from the grazing source, but decreased significantly with decreasing grazing intensity. Thus, recovery of the land from a post-threshold state may not be apparent even after 9 yr of grazing exclusion in environments with highly variable precipitation. Conclusion: The effect of exclosure duration on perennial grass cover was limited, even after controlling for environmental variability. Once a vegetation threshold has been crossed, merely removing livestock from the landscape may not be sufficient for that area to recover.

Bayesian statistics;Drought;Environmental variabil↗

NASA NTRS2019

A Bayesian Analysis of SDSS J0914+0853, a Low-mass Dual AGN Candidate

We present the first results from Bayesian AnalYsis of Multiple AGN in X-rays (BAYMAX), a tool that uses a Bayesian framework to quantitatively evaluate whether a given Chandra observation is more likely a single or dual point source. Although the most robust method of determining the presence of dual active galactic nuclei (AGNs) is to use X-ray observations, only sources that are widely separated relative to the instrumentʼs point-spread function are easy to identify. It becomes increasingly difficult to distinguish dual AGNs from single AGNs when the separation is on the order of Chandraʼs angular resolution (<1″). Using likelihood models for single and dual point sources, BAYMAX quantitatively evaluates the likelihood of an AGN for a given source. Specifically, we present results from BAYMAX analyzing the lowest-mass dual AGN candidate to date, SDSS J0914+0853, where archival Chandra data shows a possible secondary AGN ∼ 0"3 from the primary. Analyzing a new 50 ks Chandra observation, results from BAYMAX shows that SDSS J0914+0853 is most likely a single AGN with a Bayes factor of 13.5 in favor of a single point source model. Further, posterior distributions from the dual point source model are consistent with emission from a single AGN. We find a very low probability of SDSS J0914+0853 being a dual AGN system with a flux ratio f>0.3 and separation r>0"3. Overall, BAYMAX will be an important tool for correctly classifying candidate dual AGNs in the literature, as well as studying the dual AGN population where past spatial resolution limits have prevented systematic analyses.

Active galaxies↗

DOE OSTI2025

Knowledge graph-aided Bayesian active learning for top- K genetic interaction discovery

In silico methods for predicting the effects of multi-gene perturbations hold great promise for advancing functional genomics, computational drug discovery, and disease modeling. However, the development of these predictive algorithms for mammalian systems has been hampered by limited datasets and high experimental costs. In this study, we present a Bayesian active learning framework designed to discover pairwise host gene knockdowns that effectively inhibit viral proliferation in an in vitro HIV-1 infection model. Our method leverages a biological knowledge graph as side information and employs a computationally efficient batch diversification approach. We evaluated this framework using a dataset of viral load measurements obtained from multi-day dual-gene depletion experiments, encompassing all possible pairwise knockdowns of over 350 host genes associated with HIV infection. We demonstrate that our framework rapidly identifies the most effective gene knockdown pairs for reducing viral load. Furthermore, we show that incorporating side information enhances performance during the early stages of active learning (low data regime), while our batch diversification strategy significantly boosts performance in later stages (high data regime). This framework is general and can be adapted to explore gene interactions in other contexts, such as synthetic lethality prediction and mapping epistatic effects across quantitative trait loci.

Computational biology and bioinformatics↗

NASA NTRS2015

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

state estimation↗

DOE OSTI2025

Selection function of clusters in Dark Energy Survey year 3 data from cross-matching with South Pole Telescope detections

Context. Galaxy clusters selected based on overdensities of galaxies in photometric surveys provide the largest cluster samples. However, modeling the selection function of such samples is complicated by noncluster members projected along the line of sight (projection effects) and the potential detection of unvirialized objects (contamination). Aims. We empirically constrained the magnitude of these effects by cross-matching galaxy clusters selected in the Dark Energy Survey data with the redMaPPer algorithm with significant detections in three South Pole Telescope surveys (SZ, pol-ECS, pol-500d). Methods. For matched clusters, we augmented the redMaPPer catalog with the SPT detection significance. For unmatched objects we used the SPT detection threshold as an upper limit on the SZe signature. Using a Bayesian population model applied to the collected multiwavelength data, we explored various physically motivated models to describe the relationship between observed richness and halo mass. Results. Our analysis reveals a clear preference for models with an additional skewed scatter component associated with projection effects over a purely log-normal scatter model. We rule out significant contamination by unvirialized objects at the high-richness end of the sample. While dedicated simulations offer a well-fitting calibration of projection effects, our findings suggest the presence of redshift-dependent trends that these simulations may not have captured. Our findings highlight that modeling the selection function of optically detected clusters remains a complicated challenge that requires a combination of simulation and data-driven approaches.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

From chiral effective field theory to perturbative QCD: A Bayesian model mixing approach to symmetric nuclear matter

Constraining the equation of state (EOS) of strongly interacting, dense matter is the focus of intense experimental, observational, and theoretical effort. Chiral effective field theory (𝜒⁢EFT ) can describe the EOS between the typical densities of nuclei and those in the outer cores of neutron stars, while perturbative QCD (pQCD) can be applied to properties of deconfined quark matter, both with quantified theoretical uncertainties. However, describing the full range of densities in between with a single EOS that has well-quantified uncertainties is a challenging problem. Bayesian multimodel inference from 𝜒⁢EFT and pQCD can help bridge the gap between the two theories. In this work, we introduce a correlated Bayesian model mixing framework that uses a Gaussian process (GP) to assimilate different information into a single QCD EOS for symmetric nuclear matter. The present implementation uses a stationary GP to infer this mixed EOS solely from the EOSs of 𝜒⁢EFT and pQCD while accounting for the truncation errors of each theory. The GP is trained on the pressure as a function of number density in the low- and high-density regions where 𝜒⁢EFT and pQCD are, respectively, valid. We impose priors on the GP kernel hyperparameters to suppress unphysical correlations between these regimes. This, together with the assumption of stationarity, results in smooth 𝜒⁢EFT-to-pQCD curves for both the pressure and the speed of sound. We show that using uncorrelated mixing requires uncontrolled extrapolation of at least one of 𝜒⁢EFT or pQCD into regions where the perturbative series breaks down and leads to an acausal EOS. Here, we also discuss extensions of this framework to nonstationary and less differentiable GP kernels, its future application to neutron-star matter, and the incorporation of additional constraints from nuclear theory, experiment, and multimessenger astronomy.

Bayesian methods↗

NASA NTRS2003

Intelligent machines in the twenty-first century: foundations of inference and inquiry

The last century saw the application of Boolean algebra to the construction of computing machines, which work by applying logical transformations to information contained in their memory. The development of information theory and the generalization of Boolean algebra to Bayesian inference have enabled these computing machines, in the last quarter of the twentieth century, to be endowed with the ability to learn by making inferences from data. This revolution is just beginning as new computational techniques continue to make difficult problems more accessible. Recent advances in our understanding of the foundations of probability theory have revealed implications for areas other than logic. Of relevance to intelligent machines, we recently identified the algebra of questions as the free distributive algebra, which will now allow us to work with questions in a way analogous to that which Boolean algebra enables us to work with logical statements. In this paper, we examine the foundations of inference and inquiry. We begin with a history of inferential reasoning, highlighting key concepts that have led to the automation of inference in modern machine-learning systems. We then discuss the foundations of inference in more detail using a modern viewpoint that relies on the mathematics of partially ordered sets and the scaffolding of lattice theory. This new viewpoint allows us to develop the logic of inquiry and introduce a measure describing the relevance of a proposed question to an unresolved issue. Last, we will demonstrate the automation of inference, and discuss how this new logic of inquiry will enable intelligent machines to ask questions. Automation of both inference and inquiry promises to allow robots to perform science in the far reaches of our solar system and in other star systems by enabling them not only to make inferences from data, but also to decide which question to ask, which experiment to perform, or which measurement to take given what they have learned and what they are designed to understand.

Review↗