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NASA NTRS2001

The Statistical Consulting Center for Astronomy (SCCA)

The process by which raw astronomical data acquisition is transformed into scientifically meaningful results and interpretation typically involves many statistical steps. Traditional astronomy limits itself to a narrow range of old and familiar statistical methods: means and standard deviations; least-squares methods like chi(sup 2) minimization; and simple nonparametric procedures such as the Kolmogorov-Smirnov tests. These tools are often inadequate for the complex problems and datasets under investigations, and recent years have witnessed an increased usage of maximum-likelihood, survival analysis, multivariate analysis, wavelet and advanced time-series methods. The Statistical Consulting Center for Astronomy (SCCA) assisted astronomers with the use of sophisticated tools, and to match these tools with specific problems. The SCCA operated with two professors of statistics and a professor of astronomy working together. Questions were received by e-mail, and were discussed in detail with the questioner. Summaries of those questions and answers leading to new approaches were posted on the Web (www.state.psu.edu/ mga/SCCA). In addition to serving individual astronomers, the SCCA established a Web site for general use that provides hypertext links to selected on-line public-domain statistical software and services. The StatCodes site (www.astro.psu.edu/statcodes) provides over 200 links in the areas of: Bayesian statistics; censored and truncated data; correlation and regression, density estimation and smoothing, general statistics packages and information; image analysis; interactive Web tools; multivariate analysis; multivariate clustering and classification; nonparametric analysis; software written by astronomers; spatial statistics; statistical distributions; time series analysis; and visualization tools. StatCodes has received a remarkable high and constant hit rate of 250 hits/week (over 10,000/year) since its inception in mid-1997. It is of interest to scientists both within and outside of astronomy. The most popular sections are multivariate techniques, image analysis, and time series analysis. Hundreds of copies of the ASURV, SLOPES and CENS-TAU codes developed by SCCA scientists were also downloaded from the StatCodes site. In addition to formal SCCA duties, SCCA scientists continued a variety of related activities in astrostatistics, including refereeing of statistically oriented papers submitted to the Astrophysical Journal, talks in meetings including Feigelson's talk to science journalists entitled "The reemergence of astrostatistics" at the American Association for the Advancement of Science meeting, and published papers of astrostatistical content.

Akritas, Michael↗
DOE OSTI2019

Hydrogeological Model Selection Among Complex Spatial Priors

Hydrogeological field studies rely often on a single conceptual representation of the subsurface. This is problematic since the impact of a poorly chosen conceptual model on predictions might be significantly larger than the one caused by parameter uncertainty. Furthermore, conceptual models often need to incorporate geological concepts and patterns in order to provide meaningful uncertainty quantification and predictions. Consequently, several geologically realistic conceptual models should ideally be considered and evaluated in terms of their relative merits. Here, we propose a full Bayesian methodology based on Markov chain Monte Carlo to enable model selection among 2-D conceptual models that are sampled using training images and concepts from multiple-point statistics. More precisely, power posteriors for the different conceptual subsurface models are sampled using sequential geostatistical resampling and Graph Cuts. To demonstrate the methodology, we compare and rank five alternative conceptual geological models that have been proposed in the literature to describe aquifer heterogeneity at the MAcroDispersion Experiment site in Mississippi, USA. We consider a small-scale tracer test for which the spatial distribution of hydraulic conductivity impacts multilevel solute concentration data observed along a 2-D transect. The thermodynamic integration and the stepping-stone sampling methods were used to compute the evidence and associated Bayes factors using the computed power posteriors. We find that both methods are compatible with multiple-point statistics-based inversions and provide a consistent ranking of the competing conceptual models considered.

58 GEOSCIENCES↗
DOE OSTI2016

Reconstruction of elongated bubbles fusing the information from multiple optical probes through a Bayesian inference technique

In this communication, a novel optical technique has been proposed for the reconstruction of the shape of a Taylor bubble using measurements from multiple arrays of optical sensors. The deviation of an optical beam passing through the bubble depends on the contour of bubble surface. A theoretical model of the deviation of a beam during the traverse of a Taylor bubble through it has been developed. Using this model and the time history of the deviation captured by the sensor array, the bubble shape has been reconstructed. The reconstruction has been performed using an inverse algorithm based on Bayesian inference technique and Markov chain Monte Carlo sampling algorithm. The reconstructed nose shape has been compared with the true shape, extracted through image processing of high speed images. Finally, an error analysis has been performed to pinpoint the sources of the errors.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS2023

KMT-2021-BLG-1150Lb: Microlensing Planet Detected Through a Densely Covered Planetary-Caustic Signal

Aims. Recently, there have been reports of various types of degeneracies in the interpretation of planetary signals induced by planetary caustics. In this work we check whether such degeneracies persist in the case of well-covered signals by analyzing the lensing event KMT-2021-BLG-1150, the light curve of which exhibits a densely and continuously covered short-term anomaly. Methods. In order to identify degenerate solutions, we thoroughly investigated the parameter space by conducting dense grid searches for the lensing parameters. We then checked the severity of the degeneracy among the identified solutions. Results. We identify a pair of planetary solutions resulting from the well-known inner-outer degeneracy, and find that interpreting the anomaly is not subject to any degeneracy other than the inner-outer degeneracy. The measured parameters of the planet separation (normalized to the Einstein radius) and mass ratio between the lens components are ( s , q ) in ∼ (1.297, 1.10 × 10 −3 ) for the inner solution and ( s , q ) out ∼ (1.242, 1.15 × 10 −3 ) for the outer solution. According to a Bayesian estimation, the lens is a planetary system consisting of a planet with a mass M p = 0.88 +0.38 −0.36 M J and its host with a mass M h = 0.73 +0.32 −0.30 M ⊙ lying toward the Galactic center at a distance D L = 3.8 +1.3 −1.2 kpc. By conducting analyses using mock data sets prepared to mimic those obtained with data gaps and under various observational cadences, we find that gaps in data can result in various degenerate solutions, while the observational cadence does not pose a serious degeneracy problem as long as the anomaly feature can be delineated.

Gravitational microlensing↗
DOE OSTI2015

SPEQTACLE: An automated generalized fuzzy C-means algorithm for tumor delineation in PET

Purpose: Accurate tumor delineation in positron emission tomography (PET) images is crucial in oncology. Although recent methods achieved good results, there is still room for improvement regarding tumors with complex shapes, low signal-to-noise ratio, and high levels of uptake heterogeneity. Methods: The authors developed and evaluated an original clustering-based method called spatial positron emission quantification of tumor—Automatic Lp-norm estimation (SPEQTACLE), based on the fuzzy C-means (FCM) algorithm with a generalization exploiting a Hilbertian norm to more accurately account for the fuzzy and non-Gaussian distributions of PET images. An automatic and reproducible estimation scheme of the norm on an image-by-image basis was developed. Robustness was assessed by studying the consistency of results obtained on multiple acquisitions of the NEMA phantom on three different scanners with varying acquisition parameters. Accuracy was evaluated using classification errors (CEs) on simulated and clinical images. SPEQTACLE was compared to another FCM implementation, fuzzy local information C-means (FLICM) and fuzzy locally adaptive Bayesian (FLAB). Results: SPEQTACLE demonstrated a level of robustness similar to FLAB (variability of 14% ± 9% vs 14% ± 7%, p = 0.15) and higher than FLICM (45% ± 18%, p < 0.0001), and improved accuracy with lower CE (14% ± 11%) over both FLICM (29% ± 29%) and FLAB (22% ± 20%) on simulated images. Improvement was significant for the more challenging cases with CE of 17% ± 11% for SPEQTACLE vs 28% ± 22% for FLAB (p = 0.009) and 40% ± 35% for FLICM (p < 0.0001). For the clinical cases, SPEQTACLE outperformed FLAB and FLICM (15% ± 6% vs 37% ± 14% and 30% ± 17%, p < 0.004). Conclusions: SPEQTACLE benefitted from the fully automatic estimation of the norm on a case-by-case basis. This promising approach will be extended to multimodal images and multiclass estimation in future developments.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

miniTimeCube as a neutron scatter camera

We present Monte Carlo (MC) simulation results from a study of a compact plastic-scintillator detector suitable for imaging fast neutrons in the 1 – 10 MeV energy range: the miniTimeCube (mTC). Originally designed for antineutrino detection, the mTC consists of 24 MultiChannel Plate (MCP) photodetectors surrounding a 13 cm cube of boron-doped plastic scintillator. Our simulation results show that waveform digitization of 1536 optically sensitive channels surrounding the scintillator should allow for spatiotemporal determination of individual neutron-proton scatters in the detector volume to ~ 100 picoseconds and ~5 mm. A Bayesian estimation framework is presented for multiple-scatter reconstruction, and is used to estimate the incoming direction and energy of simulated individual neutrons. Finally, we show how populations of reconstructed neutrons can be used to estimate the direction and energy spectrum of nearby simulated neutron sources.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

Characterization of Proteoforms with Unknown Post-translational Modifications Using the MIScore

Various proteoforms may be generated from a single gene due to primary structure alterations (PSAs) such as genetic variations, alternative splicing, and post-translational modifications (PTMs). Top-down mass spectrometry is capable of analyzing intact proteins and identifying patterns of multiple PSAs, making it the method of choice for studying complex proteoforms. In top-down proteomics, proteoform identification is often performed by searching tandem mass spectra against a protein sequence database that contains only one reference protein sequence for each gene or transcript variant in a proteome. Because of the incompleteness of the protein database, an identified proteoform may contain unknown PSAs compared with the reference sequence. Proteoform characterization is to identify and localize PSAs in a proteoform. Although many software tools have been proposed for proteoform identification by top-down mass spectrometry, the characterization of proteoforms in identified proteoform-spectrum matches still relies mainly on manual annotation. We propose to use the Modification Identification Score (MIScore), which is based on Bayesian models, to automatically identify and localize PTMs in proteoforms. Experiments showed that the MIScore is accurate in identifying and localizing one or two modifications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

A Swing of the Pendulum: The Chemodynamics of the Local Stellar Halo Indicate Contributions from Several Radial Merger Events

We find that the chemical abundances and dynamics of APOGEE and GALAH stars in the local stellar halo are inconsistent with a scenario in which the inner halo is primarily composed of debris from a single massive, ancient merger event, as has been proposed to explain the Gaia-Enceladus/Gaia Sausage (GSE) structure. The data contain trends of chemical composition with energy that are opposite to expectations for a single massive, ancient merger event, and multiple chemical evolution paths with distinct dynamics are present. We use a Bayesian Gaussian mixture model regression algorithm to characterize the local stellar halo, and find that the data are fit best by a model with four components. We interpret these components as the Virgo Radial Merger (VRM), Cronus, Nereus, and Thamnos; however, Nereus and Thamnos likely represent more than one accretion event because the chemical abundance distributions of their member stars contain many peaks. Although the Cronus and Thamnos components have different dynamics, their chemical abundances suggest they may be related. We show that the distinct low- and high-α halo populations from Nissen & Schuster are explained by VRM and Cronus stars, as well as some in situ stars. Because the local stellar halo contains multiple substructures, different popular methods of selecting GSE stars will actually select different mixtures of these substructures, which may change the apparent chemodynamic properties of the selected stars. We also find that the Splash stars in the Solar region are shifted to higher v $\phi$ and slightly lower [Fe/H] than previously reported.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Uncertainty quantification for equations of state: copper as an example

Equations of state are essential for providing a fundamental description of materials properties in thermodynamic equilibrium and are used to provide closure relations for hydrodynamics simulations. Generally, equations of state rely on simple physics-based parameterized materials models to inform on the free energy of a material through out a given thermodynamic state space. Historically the parameters of these models have been tuned by hand to fit various experimental data. However, modern optimization and uncertainty quantification techniques allow us to quickly test thousands of parameter combinations and obtain meaningful uncertainty estimates on the parameters, opening opportunities for assessing systematic uncertainties in experiments, assessing model adequacy, and more. In this report, we use Bayesian inference to fit the solid (fcc) equation of state of copper. We focus on fitting five different experimental datasets, including the isobaric density, isobaric heat capacity, room temperature isotherm, principal isentrope, and principal Hugoniot. We fit all five data types simultaneously, and then explore the extent to which combinations of 2 subsets of the 5 datasets can constrain the EOS parameters, as compared to the fit to all 5. This information is useful for investigating the extent to which different datasets can con strain EOS models and thereby help guide experimental investigations in order to best constrain the EOS. We also discuss ways that the methodologies can be used to investigate systematic discrepancies between experiments, as well as how the methods can be used to assess model uncertainty. The framework we develop is general, in that it can be used with a variety of optimization or uncertainty quantification techniques and with a variety of data sources, including both experimental and ab-inito data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Searches for New Physics With Muon Conversion at Fermilab and Triboson Production at the LHC

We report on several efforts to search for physics beyond the standard model of particle physics at broad energy scales. The Mu2e experiment at Fermilab will search for charged lepton flavor violation via the muon to electron conversion process, which is suppressed in the Standard Model. Mu2e will be operated at a low energy, yet can probe New Physics at very high mass scales (O(1e3 - 1e4 ) TeV). At high energies, the CMS experiment at the CERN LHC continues to deliver an impressive suite of Standard Model measurements and limits on a variety of New Physics signatures. Mu2e is under construction and slated to collect its first physics data in the coming years. This thesis describes work done during the construction phase of Mu2e and focuses on two critical areas: magnetic field modeling and statistical analysis. We describe a novel method for field modeling which we validate using a simulated dataset representing the expected magnetic field in the Detector Solenoid. This method blends a standard least-squares fitting technique that utilizes physically motivated analytical model functions with a novel physics informed network that is constructed to obey Maxwell’s equations. We show the technique can model the field with an accuracy of 10−7 despite the presence of injected noise in the pseudo-measurements at the 10−5 level. We then present preliminary results of the calibration of 3D Hall probes at the sub-10−4 level. These probes will be used to directly measure the Mu2e Detector Solenoid magnetic field on a sparse grid; these measurements serve as the input to the field model fitting. Finally, we describe the first implementation of both an unbinned shape analysis and a Bayesian interpretation applied to Mu2e pseudo-data. Up to 20% tighter limits can be set by the shape analysis compared to a standard cut & count analysis. The AlCap experiment collected data at PSI in 2015 to measure several important quantities related to nuclear muon capture on an aluminum target, which is a significant background process for Mu2e. The neutron emission from muon capture can introduce background hits in the Mu2e detectors and can increase radiation damage in various elements of the apparatus. We present measurements of the neutron group fluence and mean neutron multiplicity for muon capture on aluminum nuclei. Finally, we discuss an analysis of triboson production at CMS using an Effective Field Theory framework. Standard Model triboson production, which was first observed at CMS in 2020, has a relatively small cross section and provides direct access to both anomalous triple gauge couplings and quartic gauge couplings. These couplings, interpreted in the Standard Model Effective Field Theory, are studied in the present work. We target the boosted regime where the background rate is low and yields are enhanced when dimension-6 and dimension-8 Wilson coefficients are non-zero. We do not observe an excess in the data and therefore set bounds on the Wilson coefficients. For dimension-6 coefficients the tightest observed (expected) bounds are set on cW /Λ2 where Λ is the mass scale of new physics; the bounds are [−0.13, 0.12] TeV−2 ([−0.12, 0.12] TeV−2 ) at 95% CL. The tightest bounds in dimension-8 are set on fT,0 / Λ4 ; the observed (expected) bounds at 95% CL are [−0.63, 0.69] TeV−4 ([−0.54, 0.62] TeV−4 ). Additional results are presented which include scenarios where multiple Wilson coefficients are non-zero, the application of signal model clipping to address unitarity violation in Effective Field Theories, and a novel template fit developed for easier reinterpretation of our results.

Kampa, Cole Erik [Northwestern U. (main)] (ORCID:0↗
DOE OSTI2022

Bayesian Seismoacoustic Source Location: Acoustic Approach

Seismic waves and infrasound are key technologies in the International Monitoring System (IMS) to monitor explosive events in the solid Earth and atmosphere. Energetic man-made or natural events (e.g., chemical/nuclear explosions, volcanic eruptions, and earthquakes) near the Earth’s surface produce both ground motion and atmospheric pressure disturbances which propagate as seismic waves and infrasound, respectively. Seismic waves have been generally used to detect and identify underground and near-surface events (Myers, et. al., 2007), and infrasound are sensitive to events near the surface or in the atmosphere (Modrak et. al., 2010). Due to their different sensitivities to events, they can complement to each other to improve the event detection and discrimination. The framework of joint seismoacoustic event location has recently reviewed by theoretical research (Koch and Arrowsmith, 2019). Although the early applications showed promising results to improve the accuracy of event location, their application were still limited to a small set of events selected to prove the concepts, and practical capability of the method for operational purpose is not fully evaluated with data. Our final goal is to apply the method of seismoacoustic event location to a larger set of events and evaluate its applicability for operational event location in practice. To that end, we focus on developing and verifying acoustic source location method in this study.

58 GEOSCIENCES↗
DOE OSTI2024

Ground Heat Flux Reconstruction Using Bayesian Uncertainty Quantification Machinery and Surrogate Modeling

Ground heat flux (G 0 ) is a key component of the land-surface energy balance of high-latitude regions. Despite its crucial role in controlling permafrost degradation due to global warming, G 0 is sparsely measured and not well represented in the outputs of global scale model simulation. In this study, an analytical heat transfer model is tested to reconstruct G 0 across seasons using soil temperature series from field measurements, Global Climate Model, and climate reanalysis outputs. The probability density functions of ground heat flux and of model parameters are inferred using available G 0 data (measured or modeled) for snow-free period as a reference. When observed G 0 is not available, a numerical model is applied using estimates of surface heat flux (dependent on parameters) as the top boundary condition. These estimates (and thus the corresponding parameters) are verified by comparing the distributions of simulated and measured soil temperature at several depths. Aided by state-of-the-art uncertainty quantification methods, the developed G 0 reconstruction approach provides novel means for assessing the probabilistic structure of the ground heat flux for regional permafrost change studies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Adaptive Discovery and Mixed-Variable Optimization of Next Generation Synthesizable Microelectronic Materials

Design of new microelectronic materials is characterized by several challenges such as high-dimensionality of the atomic structure-composition variable space, formidable cost of directly using high-fidelity simulations for design optimization, dispersity in literature-reported similar materials and synthesis methods, complex physical mechanisms, and mixed qualitative and quantitative design variables that lead to a disjointed design space. Even though machine learning (ML) techniques have been employed to expedite materials innovation, existing methods treat ML and design optimization as two separate processes, failing to resolve the fundamental challenges associated with high dimensionality and mixed-variable complexity. We have developed a ML enhanced mixed-variable material design optimization framework to efficiently extract useful information from existing data in literature and physics-based simulations to guide the autonomous search for optimal materials. Our proposed framework is composed of four computational modules: (1) a natural language processing (NLP) based virtual screening module, (2) classification based concept exploration module, (3) a density functional theory (DFT)-based high-fidelity evaluation model, and (4) a novel latent-variable Gaussian process (LVGP) ML model for mixed-variable problems with uncertainty quantification, which seamlessly integrates with Bayesian Optimization (BO) and achieves superb efficiency through embedded physics-based dimension reduction. Our approach is demonstrated and validated using the testbed of functional materials exhibiting metal-insulation transitions (MITs), with the targeted reversible resistivity changes (∼10^5) near room temperature. At the end of the 30-month project, we have developed a series of new ML techniques using NLP, conditional variational autoencoders, active learning, latent-variable Gaussian processes, integrated with Bayesian optimization. Our project has resulted in new predicted MITs compounds and improved understanding of MITs microscopic mechanisms, which in turn will revolutionize microelectronics science to provide energy-saving solutions. Our research has improved both creativity and efficiency in transforming rare-event discoveries of new functional materials to persistent innovations. In addition to open-sourcing the online MIT database and the classification model, the LVGP open source code has been downloaded more than 15,000 times within two years. More than 40 MIT compounds have been identified and many have been pursued experimentally via collaborators. The research results are published in close to 20 collaborative papers in high-impact journals, such as Chem. Mater., Appl. Phys. Rev., Sci. Rep., among others of design space.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Modeling the Radio Foreground for Detection of CMB Spectral Distortions from the Cosmic Dawn and the Epoch of Reionization

Cosmic baryon evolution during the Cosmic Dawn and Reionization results in redshifted 21-cm spectral distortions in the cosmic microwave background (CMB). These encode information about the nature and timing of first sources over redshifts 30–6 and appear at meter wavelengths as a tiny CMB distortion along with the Galactic and extragalactic radio sky, which is orders of magnitude brighter. Therefore, detection requires precise methods to model foregrounds. We present a method of foreground fitting using maximally smooth (MS) functions. We demonstrate the usefulness of MS functions over traditionally used polynomials to separate foregrounds from the Epoch of Reionization (EoR) signal. We also examine the level of spectral complexity in plausible foregrounds using GMOSS, a physically motivated model of the radio sky, and find that they are indeed smooth and can be modeled by MS functions to levels sufficient to discern the vanilla model of the EoR signal. We show that MS functions are loss resistant and robustly preserve EoR signal strength and turning points in the residuals. Finally, we demonstrate that in using a well-calibrated spectral radiometer and modeling foregrounds with MS functions, the global EoR signal can be detected with a Bayesian approach with 90% confidence in 10 minutes’ integration.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Quantification of uncertainty in photon source spot size inference during laser-driven radiography experiments at TRIDENT

Images of the R2DTO resolution target were obtained during laser-driven-radiography experiments performed at the TRIDENT laser facility, and analysis of these images using the Bayesian Inference Engine (BIE) determines a most probable full-width half maximum (FWHM) spot size of 78 μm. However, significant uncertainty prevails due to variation in the measured detector blur. Propagating this uncertainty in detector blur through the forward model results in an interval of probabilistic ambiguity spanning approximately 35-195 μm when the laser energy impinges on a thick (1 mm) tantalum target. In other phases of the experiment, laser energy is deposited on a thin (~100 nm) aluminum target placed 250 μm ahead of the tantalum converter. When the energetic electron beam is generated in this manner, upstream from the bremsstrahlung converter, the inferred spot size shifts to a range of much larger values, approximately 270-600 μm FWHM. This report discusses methods applied to obtain these intervals as well as concepts necessary for interpreting the result within a context of probabilistic quantitative inference.

47 OTHER INSTRUMENTATION↗
DOE OSTI2019

Recommended nuclear data for medical radioisotope production: diagnostic positron emitters

An IAEA coordinated research project that began in 2012 and ended in 2016 was primarily dedicated to the compilation, evaluation and recommendation of cross-section data for the production of medical radionuclides. One significant part of this work focused on diagnostic positron emitters. These particular studies consist of 69 reactions for direct and indirect or generator production of 44 Sc( 44 Ti), 52 mMn( 52 Fe), 52 gMn, 55 Co, 61 Cu, 62 Cu( 62 Zn), 66 Ga, 68 Ga( 68 Ge), 72 As( 72 Se), 73 Se, 76 Br, 82 Rb( 82 Sr), 82 mRb, 86 Y, 89 Zr, 90 Nb, 94 mTc, 110 mIn( 110 Sn), 118 Sb( 118 Te), 120 I, 122 I( 122 Xe), 128 Cs( 128 Ba), and 140 Pr( 140 Nd) medical radionuclides. The resulting reference cross-section data were obtained from Padé fits to selected and corrected experimental data, and integral thick target yields were subsequently deduced. Uncertainties in the fitted results were estimated via a Padé least-squares method with the addition of a 4% assessed systematic uncertainty. Experimental data were also compared with theoretical predictions available from the TENDL-2015 and TENDL-2017 libraries.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2015

Probing cosmology and gravity with redshift-space distortions around voids

Cosmic voids in the large-scale structure of the Universe affect the peculiar motions of objects in their vicinity. Although these motions are difficult to observe directly, the clustering pattern of their surrounding tracers in redshift space is influenced in a unique way. This allows to investigate the interplay between densities and velocities around voids, which is solely dictated by the laws of gravity. With the help of N-body simulations and derived mock-galaxy catalogs we calculate the average density fluctuations around voids identified with a watershed algorithm in redshift space and compare the results with the expectation from general relativity and the ΛCDM model. We find linear theory to work remarkably well in describing the dynamics of voids. Adopting a Bayesian inference framework, we explore the full posterior of our model parameters and forecast the achievable accuracy on measurements of the growth rate of structure and the geometric distortion through the Alcock-Paczyński effect. Systematic errors in the latter are reduced from ∼15% to ∼5% when peculiar velocities are taken into account. The relative parameter uncertainties in galaxy surveys with number densities comparable to the SDSS MAIN (CMASS) sample probing a volume of 1h{sup −3}Gpc{sup 3} yield σ{sub f/b}/(f/b).∼2% (20%) and σ{sub D{sub A{sub H}}}/D{sub AH∼0}.2% (2%), respectively. At this level of precision the linear-theory model becomes systematics dominated, with parameter biases that fall beyond these values. Nevertheless, the presented method is highly model independent; its viability lies in the underlying assumption of statistical isotropy of the Universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Quantifying correlated truncation errors in effective field theory

Effective field theories (EFTs) organize the description of complex systems into an infinite sequence of decreasing importance. Predictions are made with a finite number of terms, which induces a truncation error that is often left unquantified. Here, we formalize the notion of EFT convergence and propose a Bayesian truncation error model for predictions that are correlated across the independent variables, e.g., energy or scattering angle. Central to our approach are Gaussian processes that encode both the naturalness and correlation structure of EFT coefficients. Our use of Gaussian processes permits efficient and accurate assessment of credible intervals, allows EFT fits to easily include correlated theory errors, and provides analytic posteriors for physical EFT-related quantities such as the expansion parameter. Furthermore, we demonstrate that model-checking diagnostics—applied to the case of multiple curves—are powerful tools for EFT validation. As an example, we assess a set of nucleon-nucleon scattering observables in chiral EFT. In an effort to be self-contained, appendices include thorough derivations of our statistical results. Our methods are packaged in Python code, called gsum, that is available for download on GitHub.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗