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DOE OSTI2024

Assessing and benchmarking the fidelity of posterior inference methods for astrophysics data analysis

In this era of large and complex astronomical survey data, interpreting, validating, and comparing inference techniques becomes increasingly difficult. This is particularly critical for emerging inference methods like Simulation-Based Inference (SBI), which offer significant speedup potential and posterior modeling flexibility, especially when deep learning is incorporated. We present a study to assess and compare the performance and uncertainty prediction capability of Bayesian inference algorithms – from traditional MCMC sampling of analytic functions to deep learning-enabled SBI. We focus on testing the capacity of hierarchical inference modeling in those scenarios. Before we extend this study to cosmology, we first use astrophysical simulation data to ensure interpretability. We demonstrate a probabilistic programming implementation of hierarchical and non-hierarchical Bayesian inference using simulations derived from the DeepBench software library, a benchmarking tool developed by our group that generates simple and controllable astrophysical objects from first principles. This study will enable astronomers and physicists to harness the inference potential of these methods with confidence.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

A Bayesian Monte Carlo inversion of spatial auto-correlation (SPAC) for near-surface Vs structure applied to both broad-band and geophone data

SUMMARY We propose a new Bayesian method to reveal the Vs structure of the near surface of the earth using spatial autocorrelation (SPAC) functions and apply this new method to synthetic, broad-band and geophone data sets. The principle of SPAC is introduced, and an implementation of the Bayesian Monte Carlo inversion (BMCI) for modelling SPAC coherency functions is described. To demonstrate its effectiveness, BMCI is applied to synthetic tests, data from 14 SPAC array sites in the Salt Lake Valley (SLV), Utah, and two arrays (one broad-band and one geophone) located in south central Utah. The Vs models derived from previous SPAC analysis of the 14 SLV sites differ by 10 per cent at most from those determined by BMCI and lie within uncertainties determined for the BMCI models. These agreements demonstrate the effectiveness of the BMCI method. The synthetic tests and applications to the SLV SPAC data show BMCI has great potential to resolve Vs structure down to at least 400 m. To achieve resolution for deeper Vs structure, longer duration deployments, wider array apertures, and additional seismometers or geophones can be used. Additionally, when the target frequencies are greater than 0.1 Hz, there is no apparent disadvantage in using geophone data for BMCI compared to broad-band data. Most significantly, BMCI places a quantifiable constraint on the uncertainties of the Vs models as well as Vs30.

58 GEOSCIENCES↗
DOE OSTI2024

Inverter Model Validation and Calibration Using Phasor Measurement Unit Data

As the penetration of inverter-based renewable energy resources increases in the power grid, especially at the distribution and microgrid levels, the need to accurately represent them in planning studies increases as well. However, due to the lack of well-established standard procedures, and vendor reluctance towards the detailed sharing of proprietary models, automated dynamic model validation and parameter calibration tools for inverter based resources (IBRs) remain scarce. This work presents a model validation and parameter calibration platform for representing IBRs with generic phasor-domain models. Phasor measurements of power system events are used for continuous validation using the data playback method, and model parameters are re-calibrated if a significant mismatch between measurements and model response is observed. Unique features of the proposed platform include- (a) an iterative Bayesian optimization approach towards parameter calibration to address a possible mismatch between the structures of generic models implemented in simulation softwares and actual commercial inverters, (b) error metrics designed to account for a possible mismatch between the time resolution of simulation and measurements, and (c) analysis of the measurement-simulation mismatch to provide guidance to engineering personnel regarding model shortcomings. The performance of the platform has been illustrated using both simulated data and field measurements to validate/calibrate inverter models in GridLAB-D.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2018

Voltron Compatible Whole Building Root-Fault Detection and Diagnosis

Buildings consume more than 40% of primary energy in the U.S. Malfunctioning sensors, components, and control systems, as well as degrading components in Heating, Ventilating and Air-conditioning (HVAC) and lighting systems are main reasons for energy waste and unsatisfactory indoor environment. Field studies have shown that an energy saving of 5-30% of total building energy consumption and improved indoor air quality can be achieved by simply applying automated fault detection and diagnosis (AFDD), followed by corrections even if these are not done in real time. Extensive research has been made on the development of component level AFDD tools in the past two decades. However, in recent years, the development of method for a whole building level AFDD has received much attention. Here, a whole building fault refers to a fault happening in one subsystem but impact on more than one subsystems, or has a significant impact on building performances, such as building’s energy consumption. Existing component level AFDD tools could fail to detect or give false alarm for faults that trigger abnormalities in multiple subsystems. Isolating such whole building faults, which have impacts on multiple subsystems, is also challenging by simply using component based AFDD solutions. On the other hand, it might be more cost-effective for medium- or small-sized commercial buildings that have subsystems (e.g. primary cooling subsystem, air loop subsystem, heating subsystem, lighting subsystem, etc.) to install one whole building level AFDD tool, rather than many component level AFDD tools, to focus on significant faults. The focus of this project is firstly to provide training opportunities in building AFDD research area for undergraduate students and to develop a workforce pipeline in building sciences. The objective of the proposed research activities is to develop cost-effective and scalable AFDD solutions for whole building level faults. The developed AFDD solution is VOLTTRONTM compatible to further increase its plug-n-play capacity and the market penetration. VOLTTRONTM is an open-source innovative distributed control and sensing software platform developed by the Pacific Northwest National Laboratory. A VOLTTRONTM compatible AFDD tool brings the benefits such as low-cost deployment, and better building to grid integration, etc. The performance of the developed whole building AFDD tools is evaluated using data collected from a mixed-use medium-sized university campus building. Another significant goal of this project is to engage undergraduate students in research activities and expose them to building control and AFDD fields. A demonstration building – Nesbitt Hall at Drexel University is identified for this study. This demonstration building has a typical HVAC system configuration, which includes a water-cooled chiller system, three variable air volume (VAV) air handling unit (AHU) systems, and a hydronic heating system. Faults, that are expected to have a whole building level impact, are artificially implemented in this demonstration building for three different seasons. Building data have been collected in this project, which include fault free building automation system (BAS) data and BAS data that contain system behaviors caused by artificially implemented and naturally occurred faults. These collected data are used to evaluate the developed whole building AFDD tools. A data-driven method, which includes a weather and schedule-based pattern matching (WPM) method and Feature based Principal Component Analysis (FPCA) method, is developed for whole building level fault detection. Parameter sensitivity tests, including snapshot window size, data sample searching pool size, etc., are implemented to evaluate the impacts of various WPM-FPCA parameters. A data-driven and expert knowledge/rule-based method using Bayesian Network (BN) and WPM is developed for whole building level fault diagnosis. The developed WPM-BN method, which includes a two-layer BN structure model and BN parameters, are either learned from baseline data or developed from expert knowledge. The developed whole building AFDD tools are evaluated using BAS data collected from the demonstration building. Using the evaluation data set, the WPM-FPCA fault detection method is evaluated under two different Principle Component (PC) retention rates, i.e., 0.65 retention rate and 0.95 retention rate. It is observed that when using 0.65 PC retention rate, the WPM-FPCA fault detection method achieves a 79% fault detection rate (this rate reaches to 85% when including the six make-up fault test cases discussed in the next bullet), while when using 0.95 PC retention rate, the WPM-FPCA fault detection method achieves 100% fault detection rate (this rate remains to be 100% when including the six make-up fault test cases). Under both PC retention rates, the WPM-FPCA fault detection method demonstrates 0% false alarm rates. Using the evaluation data set, the developed WPM-BN fault diagnosis method has successfully diagnosed thirteen (13) faults out of the fourteen (14) fault test cases. The one mis-diagnosed case exhibits fewer fault symptoms in different subsystems, when compared with other fault test cases. Overall speaking, the developed whole building AFDD solutions demonstrate satisfactory fault detection/diagnosis accuracy with very low false alarm rate. Lastly, a survey and market study has been performed to understand the existing AFDD market, including its gaps and needs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2018

Accidental Father-to-Son HIV-1 Transmission During the Seroconversion Period

A 4-year-old child born to an HIV-1 seronegative mother was diagnosed with HIV-1, the main risk factor being transmission from the child's father who was seroconverting at the time of the child's birth. In the context of a forensic investigation, here we aimed to identify the source of infection of the child and date of the transmission event. Samples were collected from the father and child at two time points about 4 years after the child's birth. Partial segments of three HIV-1 genes (gag, pol, and env) were sequenced and maximum likelihood (ML) and Bayesian methods were used to determine direction and estimate date of transmission. Neutralizing antibodies were determined using a single cycle assay. Bayesian trees displayed a paraphyletic–monophyletic topology in all three genomic regions, with the father's host label at the root, which is consistent with father-to-son transmission. ML trees found similar topologies in gag and pol and a monophyletic–monophyletic topology in env. Analysis of the time of the most recent common ancestor of each HIV-1 gene population indicated that the child was infected shortly after the father. Consistent with the infection history, both father and son developed broad and potent HIV-specific neutralizing antibody responses. In conclusion, the direction of transmission implicated the father as the source of transmission. Transmission occurred during the seroconversion period when the father was unaware of the infection and was likely accidental. This case shows how genetic, phylogenetic, and serological data can contribute for the forensic investigation of HIV transmission.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

In Situ Inference for Earth System Predictability

An understanding of future evolution in precipitation extremes is critical to numerous DOE mission questions. Extreme events are by nature short time-scale events that are difficult to diagnose in available model data. Accurate modeling of extreme events necessarily requires high spatial resolution at the storm scale locally. However, the environment in which storms grow is dependent on global, remote, processes. These complex spatiotemporal relationships are impossible to diagnose at resolutions required to accurately model storms responsible for extreme precipitation. At exascale, climate simulations will produce results at fine enough resolution to investigate these relationships. However, the resulting data from these simulations will be far too large to save for post-simulation analysis. We advocate for fitting statistical models inside the simulations as they run, a context known as in situ, which will facilitate scientific investigations using the full fine-scale data stream. Figure 1 shows an example of the type of model we could consider, a Bayesian hierarchical spatial regression model. Precipitation extremes at each grid cell are modeled using extreme value distributions. Since extremes are rare, fitting models to individual grid cells can result in high variance and poor estimates. Instead, the model can be made more robust by smoothing the parameters of the extreme value model across space. Additionally, the parameters themselves can be functionally linked to other variables elsewhere in the simulation. Thus, we can use the fine-scale data to build more robust models for extremes that link extreme behavior to other climate patterns.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

In Situ Inference for Earth System Predictability

Focal Area: Focal Area 3: Insight gleaned from complex simulated data using AI, big data analytics, and other advanced methods, including explainable AI and physics- or knowledge-guided AI. Science Challenge: An understanding of future evolution in precipitation extremes is critical to numerous DOE mission questions. Extreme events are by nature short time-scale events that are difficult to diagnose in available model data. Accurate modeling of extreme events necessarily requires high spatial resolution at the storm scale locally. However, the environment in which storms grow is dependent on global, remote, processes. These complex spatiotemporal relationships are impossible to diagnose at resolutions required to accurately model storms responsible for extreme precipitation. At exascale, climate simulations will produce results at fine enough resolution to investigate these relationships. However, the resulting data from these simulations will be far too large to save for post-simulation analysis. We advocate for fitting statistical models inside the simulations as they run, a context known as in situ, which will facilitate scientific investigations using the full fine-scale data stream. Figure 1 shows an example of the type of model we could consider, a Bayesian hierarchical spatial regression model. Precipitation extremes at each grid cell are modeled using extreme value distributions. Since extremes are rare, fitting models to individual grid cells can result in high variance and poor estimates. Instead, the model can be made more robust by smoothing the parameters of the extreme value model across space. Additionally, the parameters themselves can be functionally linked to other variables elsewhere in the simulation. Thus, we can use the fine-scale data to build more robust models for extremes that link extreme behavior to other climate patterns.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Embedded Error Bayesian Calibration of Thermal Decomposition of Organic Materials

Organic materials are an attractive choice for structural components due to their light weight and versatility. However, because they decompose at low temperatures relative to tradiational materials they pose a safety risk due to fire and loss of structural integrity. To quantify this risk, analysts use chemical kinetics models to describe the material pyrolysis and oxidation using thermogravimetric analysis. This process requires the calibration of many model parameters to closely match experimental data. Previous efforts in this field have largely been limited to finding a single best-fit set of parameters even though the experimental data may be very noisy. Furthermore the chemical kinetics models are often simplified representations of the true de- composition process. The simplification induces model-form errors that the fitting process cannot capture. In this work we propose a methodology for calibrating decomposition models to thermogravimetric analysis data that accounts for uncertainty in the model-form and experimental data simultaneously. The methodology is applied to the decomposition of a carbon fiber epoxy composite with a three-stage reaction network and Arrhenius kinetics. The results show a good overlap between the model predictions and thermogravimetric analysis data. Uncertainty bounds capture devia- tions of the model from the data. The calibrated parameter distributions are also presented. In conclusion, the distributions may be used in forward propagation of uncertainty in models that leverage this material.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Play fairway analysis of geothermal resources across the state of Hawaii: 2. Resource probability mapping

We develop a new geostatistical method to combine evidence provided by diverse geological data sets and produce maps of geothermal resource probability. The application is to the State of Hawaii, and the data sets include the locations and ages of mapped volcanic centers, gravity and magnetotelluric measurements, groundwater temperature and geochemistry, ground surface deformation, seismicity, water table elevation, and groundwater recharge. Using the basic principles of Bayesian statistics, these data and expert knowledge about the effects and importance of the data are used to compute the probabilities of the primary resource qualities of elevated subsurface heat, reservoir permeability, and reservoir fluid content. The product of these marginal probabilities estimates the joint probability of all three qualities and hence the probability of a successful geothermal prospect at each map point. An analogous set of algorithms is used to quantify the confidence in the probability at each point. Not surprisingly, we find that successful geothermal prospects are most probable on the active volcanoes of Hawaii Island, including the area of Hawaii’s single geothermal energy plant. Probability decreases primarily with shield volcano age, being relatively moderate in select locations on Maui and Lanai, relatively low on Oahu, and minimal on Kauai. Future exploration efforts should consider these results as well as the practical, societal, and economic conditions that influence development viability. Here, the difficulties of interisland power transmission mean that even areas with moderate to low probabilities are worth investigating on islands with population centers.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Measuring the robustness of predictive probability for early stopping in two-group comparisons

We report physical experiments are often expensive and time-consuming. Test engineers must certify the compatibility of aircraft and their weapon systems before they can be deployed in the field, but the testing required is time consuming, expensive, and resource limited. Adopting Bayesian adaptive designs is a promising way to borrow from the successes seen in the clinical trials domain. The use of predictive probability (PP) to stop testing early and make faster decisions is particularly appealing given the aforementioned constraints. Given the high-consequence nature of the tests performed in the national security space, a strong understanding of new methods is required before being deployed. Although PP has been thoroughly studied for binary data, there is less work with continuous data, where many reliability studies are interested in certifying the specification limits of components. A simulation study evaluating the robustness of this approach indicates early stopping based on PP is reasonably robust to minor assumption violations, especially when only a few interim analyses are conducted. The simulation study also compares PP to conditional power, showing its relative strengths and weaknesses. A post-hoc analysis exploring whether release requirements of a weapon system from an aircraft are within specification with desired reliability resulted in stopping the experiment early and saving 33% of the experimental runs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Attributing runoff changes to climate variability and human activities: Uncertainty analysis using four monthly water balance models

Hydrological simulations to delineate the impacts of climate variability and human activities are subjected to uncertainties related to both parameter and structure of the hydrological models. To analyze the impact of these uncertainties on the model performance and to yield more reliable simulation results, a global calibration and multimodel combination method that integrates the Shuffled Complex Evolution Metropolis (SCEM) and Bayesian Model Averaging (BMA) of four monthly water balance models was proposed. The method was applied to the Weihe River Basin (WRB), the largest tributary of the Yellow River, to determine the contribution of climate variability and human activities to runoff changes. The change point, which was used to determine the baseline period (1956-1990) and human-impacted period (1991-2009), was derived using both cumulative curve and Pettitt’s test. Results show that the combination method from SCEM provides more skillful deterministic predictions than the best calibrated individual model, resulting in the smallest uncertainty interval of runoff changes attributed to climate variability and human activities. This combination methodology provides a practical and flexible tool for attribution of runoff changes to climate variability and human activities by hydrological models.

runoff change, uncertainty assessment, monthly wat↗
DOE OSTI2017

The weighted priors approach for combining expert opinions in logistic regression experiments

When modeling the reliability of a system or component, it is not uncommon for more than one expert to provide very different prior estimates of the expected reliability as a function of an explanatory variable such as age or temperature. Our goal in this paper is to incorporate all information from the experts when choosing a design about which units to test. Bayesian design of experiments has been shown to be very successful for generalized linear models, including logistic regression models. We use this approach to develop methodology for the case where there are several potentially non-overlapping priors under consideration. While multiple priors have been used for analysis in the past, they have never been used in a design context. The Weighted Priors method performs well for a broad range of true underlying model parameter choices and is more robust when compared to other reasonable design choices. Finally, we illustrate the method through multiple scenarios and a motivating example. Additional figures for this article are available in the online supplementary information.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Joint Planck and WMAP assessment of low CMB multipoles

The remarkable progress in cosmic microwave background (CMB) studies over past decade has led to the era of precision cosmology in striking agreement with the ΛCDM model. However, the lack of power in the CMB temperature anisotropies at large angular scales (low-ℓ), as has been confirmed by the recent Planck data also (up to 0ℓ=4), although statistically not very strong (less than 3σ), is still an open problem. One can avoid to seek an explanation for this problem by attributing the lack of power to cosmic variance or can look for explanations i.e., different inflationary potentials or initial conditions for inflation to begin with, non-trivial topology, ISW effect etc. Features in the primordial power spectrum (PPS) motivated by the early universe physics has been the most common solution to address this problem. In the present work we also follow this approach and consider a set of PPS which have features and constrain the parameters of those using WMAP 9 year and Planck data employing Markov-Chain Monte Carlo (MCMC) analysis. The prominent feature of all the models of PPS that we consider is an infra-red cut off which leads to suppression of power at large angular scales. We consider models of PPS with maximum three extra parameters and use Akaike information criterion (AIC) and Bayesian information criterion (BIC) of model selection to compare the models. For most models, we find good constraints for the cut off scale k{sub c}, however, for other parameters our constraints are not that good. We find that sharp cut off model gives best likelihood value for the WMAP 9 year data, but is as good as power law model according to AIC. For the joint WMAP 9 + Planck data set, Starobinsky model is slightly preferred by AIC which is also able to produce CMB power suppression up to 0ℓ≤3 to some extent. However, using BIC criteria, one finds model(s) with least number of parameters (power law model) are always preferred.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Modeling the He II Transverse Proximity Effect: Constraints on Quasar Lifetime and Obscuration

The He II transverse proximity effect - enhanced He II Lyα transmission in a background sightline caused by the ionizing radiation of a foreground quasar - offers a unique opportunity to probe the emission properties of quasars, in particular the emission geometry (obscuration, beaming) and the quasar lifetime. Building on the foreground quasar survey published in Schmidt et al., we present a detailed model of the He II transverse proximity effect, specifically designed to include light travel time effects, finite quasar ages, and quasar obscuration. Here, we post-process outputs from a cosmological hydrodynamical simulation with a fluctuating He ii ultraviolet background model, with the added effect of the radiation from a single bright foreground quasar. We vary the age t age and obscured sky fractions Ω obsc of the foreground quasar, and explore the resulting effect on the He ii transverse proximity effect signal. Fluctuations in intergalactic medium density and the ultraviolet background, as well as the unknown orientation of the foreground quasar, result in a large variance of the He II Lyα transmission along the background sightline. We develop a fully Bayesian statistical formalism to compare far-ultraviolet He ii Lyα transmission spectra of the background quasars to our models, and extract joint constraints on t age and Ω obsc for the six Schmidt et al. foreground quasars with the highest implied He II photoionization rates. Our analysis suggests a bimodal distribution of quasar emission properties, whereby one foreground quasar, associated with a strong He II transmission spike, is relatively old (22 Myr) and unobscured (Ω obsc < 35%), whereas three others are either younger than 10 Myr or highly obscured (Ω obsc > 70%).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

MOOSE ProbML: Parallelizable Probabilistic Machine Learning and Uncertainty Quantification Capabilities

The Multiphysics Object Oriented Simulation Environment (MOOSE) is a widely used open- source finite element software for performing multiphysics multiscale simulations in a massively parallel fashion. Recently, the computational team at Idaho National Laboratory (INL) has implemented Probabilistic Machine Learning (ProbML) capabilities in MOOSE—in a parallelized fashion—and enable active learning with large-scale computational models for tasks such as surrogate model development, scale bridging, forward/inverse uncertainty quantification (UQ), Bayesian optimization, etc. This presentation summarizes these developments in MOOSE along with demonstrations on several real applications relevant to nuclear energy. At the fundamental level, samplers like Monte Carlo/Latin Hypercube, variance reduction, parallelized Markov Chain Monte Carlo (MCMC) support uncertainty propagation in both forward and inverse settings. These samplers can be integrated with the Gaussian processes (GP) suite in MOOSE, which offer several variants like scalar GPs, multi-output GPs, and deep GPs, to enable active learning. These GPs can be tuned using gradient-based optimization methods like Adam and its variants or gradient-free methods like the elliptical slice sampler (a variant of MCMC adept under Gaussian settings) for more complex covariance kernels or likelihoods whose gradient computations can be cumbersome. A variety of batch acquisition functions permit parallelized evaluation of the computational model and support different learning objectives with high efficiency like Bayesian inference, global surrogate development, optimization, etc. Furthermore, libtorch integration supports training, evaluation, and re-training of neural networks and other complex machine learning models in active learning settings. The impacts of these developments are shown on several real applications: (1) nuclear fuel inverse UQ and model inadequacy assessment using the Kennedy O’Hagan framework; (2) uncertainty aware surrogate modeling for additive manufacturing to predict field quantities; (3) nuclear reactor rare events analysis; and (4) complex fluid flow prediction using a global surrogate with quantified prediction uncertainty. Finally, the outlook of MOOSE ProbML is discussed for both outer-loop and inner-loop computations in the broad view to accelerate fuels and materials qualification, address gaps in knowledge and data, and assess new reactor/fuel systems.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

CLASH: JOINT ANALYSIS OF STRONG-LENSING, WEAK-LENSING SHEAR, AND MAGNIFICATION DATA FOR 20 GALAXY CLUSTERS

We present a comprehensive analysis of strong-lensing, weak-lensing shear and magnification data for a sample of 16 X-ray-regular and 4 high-magnification galaxy clusters at 0.19≲z≲0.69 selected from Cluster Lensing And Supernova survey with Hubble (CLASH). Our analysis combines constraints from 16-band Hubble Space Telescope observations and wide-field multi-color imaging taken primarily with Suprime-Cam on the Subaru Telescope, spanning a wide range of cluster radii (10″–16′). We reconstruct surface mass density profiles of individual clusters from a joint analysis of the full lensing constraints, and determine masses and concentrations for all of the clusters. We find the internal consistency of the ensemble mass calibration to be ≤5% ± 6% in the one-halo regime (200–2000 kpc h{sup −1}) compared to the CLASH weak-lensing-only measurements of Umetsu et al. For the X-ray-selected subsample of 16 clusters, we examine the concentration–mass (c–M) relation and its intrinsic scatter using a Bayesian regression approach. Our model yields a mean concentration of c|{sub z=0.34}=3.95±0.35 at M{sub 200c} ≃ 14 × 10{sup 14} M{sub ⊙} and an intrinsic scatter of σ(lnc{sub 200c})=0.13±0.06, which is in excellent agreement with Λ cold dark matter predictions when the CLASH selection function based on X-ray morphological regularity and the projection effects are taken into account. We also derive an ensemble-averaged surface mass density profile for the X-ray-selected subsample by stacking their individual profiles. The stacked lensing signal is detected at 33σ significance over the entire radial range ≤4000 kpc h{sup −1}, accounting for the effects of intrinsic profile variations and uncorrelated large-scale structure along the line of sight. The stacked mass profile is well described by a family of density profiles predicted for cuspy dark-matter-dominated halos in gravitational equilibrium, namely, the Navarro–Frenk–White (NFW), Einasto, and DARKexp models, whereas the single power-law, cored isothermal and Burkert density profiles are disfavored by the data. We show that cuspy halo models that include the large-scale two-halo term provide improved agreement with the data. For the NFW halo model, we measure a mean concentration of c{sub 200c}=3.79{sub −0.28}{sup +0.30} at M{sub 200c}=14.1{sub −1.0}{sup +1.0}×10{sup 14} M{sub ⊙}, demonstrating consistency between the complementary analysis methods.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Investigation of methodology for uncertainty quantification of model parameters

Quantifying the uncertainty contributors of best-estimate thermal hydraulic code is getting more and more attention in safety analysis of nuclear industry during recent decades. Yet for uncertainties of certain model parameters which may not be directly measured, the quantification process is usually subjective and inaccurate. This paper investigates the statistical methodologies in order to get the probability density function (pdf) of model parameters more objectively based on observed experimental responses. The simplification of mathematical model is described for the parameter estimation, and solutions based on Bayesian theorem and Maximum Likelihood Estimation (MLE) are classified and demonstrated for both deterministic approach and stochastic approach. As an application, the uncertainties of model parameters related to reflood phenomena implemented in RELAP5 code are quantified. It is indicated that the statistical method which is independent of best-estimate code is feasible and easy to apply. And through the check of uncertainty propagation, it demonstrates that the uncertainty bands can envelope most of the experiment measurement with advantage of accuracy. (authors)

42 ENGINEERING↗
DOE OSTI2023

BEYONDPLANCK XIV. Polarized foreground emission between 30 and 70 GHz

We constrain polarized foreground emission between 30 and 70 GHz with the Planck Low Frequency Instrument (LFI) and WMAP data within the global Bayesian BeyondPlanck framework. We combine for the first time full-resolution Planck LFI time-ordered data with low-resolution WMAP sky maps at 33, 40 and 61 GHz. Spectral parameters are fit with a likelihood defined at the native resolution of each frequency channel. This analysis represents the first implementation of true multi-resolution component separation applied to CMB observations for both amplitude and spectral energy distribution (SED) parameters. For synchrotron emission, we approximate the SED as a power-law in frequency and find that the low signal-to-noise ratio of the current data strongly limits the number of free parameters that may be robustly constrained. We partition the sky into four large disjoint regions (High Latitude; Galactic Spur; Galactic Plane; and Galactic Center), each associated with its own power-law index. We find that the High Latitude region is prior-dominated, while the Galactic Center region is contaminated by residual instrumental systematics. The two remaining regions appear to be signal-dominated, and for these we derive spectral indices of $β$ S Spur = -3.17 ± 0.06 and $β$ S Plane = -3.03 ± 0.07, in good agreement with previous results. For thermal dust emission we assume a modified blackbody model and we fit a single power-law index across the full sky. We find $β$ d = 1.64 ± 0.03, which is slightly steeper than reported from Planck HFI data, but still statistically consistent at the 2σ confidence level.

79 ASTRONOMY AND ASTROPHYSICS↗