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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

BEYONDPLANCK IV. On end-to-end simulations in CMB analysis — Bayesian versus frequentist statistics

End-to-end simulations play a key role in the analysis of any high-sensitivity cosmic microwave background (CMB) experiment, providing high-fidelity systematic error propagation capabilities that are unmatched by any other means. In this paper, we address an important issue regarding such simulations, namely, how to define the inputs in terms of sky model and instrument parameters. These may either be taken as a constrained realization derived from the data or as a random realization independent from the data. We refer to these as posterior and prior simulations, respectively. We show that the two options lead to significantly different correlation structures, as prior simulations (contrary to posterior simulations) effectively include cosmic variance, but they exclude realization-specific correlations from non-linear degeneracies. Consequently, they quantify fundamentally different types of uncertainties. We argue that as a result, they also have different and complementary scientific uses, even if this dichotomy is not absolute. In particular, posterior simulations are in general more convenient for parameter estimation studies, while prior simulations are generally more convenient for model testing. Before BEYONDPLANCK, most pipelines used a mix of constrained and random inputs and applied the same hybrid simulations for all applications, even though the statistical justification for this is not always evident. BEYONDPLANCK represents the first end-to-end CMB simulation framework that is able to generate both types of simulations and these new capabilities have brought this topic to the forefront. The BEYONDPLANCK posterior simulations and their uses are described extensively in a suite of companion papers. In this work, we consider one important applications of the corresponding prior simulations, namely, code validation. Specifically, we generated a set of one-year LFI 30 GHz prior simulations with known inputs and we used these to validate the core low-level BEYONDPLANCK algorithms dealing with gain estimation, correlated noise estimation, and mapmaking.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

An implementation of neural simulation-based inference for parameter estimation in ATLAS

Neural simulation-based inference (NSBI) is a powerful class of machine-learning-based methods for statistical inference that naturally handles high-dimensional parameter estimation without the need to bin data into low-dimensional summary histograms. Such methods are promising for a range of measurements, including at the Large Hadron Collider, where no single observable may be optimal to scan over the entire theoretical phase space under consideration, or where binning data into histograms could result in a loss of sensitivity. This work develops a NSBI framework for statistical inference, using neural networks to estimate probability density ratios, which enables the application to a full-scale analysis. It incorporates a large number of systematic uncertainties, quantifies the uncertainty due to the finite number of events in training samples, develops a method to construct confidence intervals, and demonstrates a series of intermediate diagnostic checks that can be performed to validate the robustness of the method. As an example, the power and feasibility of the method are assessed on simulated data for a simplified version of an off-shell Higgs boson couplings measurement in the four-lepton final states. This approach represents an extension to the standard statistical methodology used by the experiments at the Large Hadron Collider, and can benefit many physics analyses.

frequentist statistics↗
DOE OSTI2020

The look-elsewhere effect from a unified Bayesian and frequentist perspective

When searching over a large parameter space for anomalies such as events, peaks, objects, or particles, there is a large probability that spurious signals with seemingly high signi ficance will be found. This is known as the look-elsewhere effect and is prevalent throughout cosmology, (astro)particle physics, and beyond. To avoid making false claims of detection, one must account for this effect when assigning the statistical significance of an anomaly. This is typically accomplished by considering the trials factor, which is generally computed numerically via potentially expensive simulations. In this paper we develop a continuous generalization of the Bonferroni and Sidak corrections by applying the Laplace approximation to evaluate the Bayes factor, and in turn relating the trials factor to the prior-to-posterior volume ratio. Here, we use this to define a test statistic whose frequentist properties have a simple interpretation in terms of the global p-value, or statistical significance. We apply this method to various physics-based examples and show it to work well for the full range of p-values, i.e. in both the asymptotic and non-asymptotic regimes. We also show that this method naturally accounts for other model complexities such as additional degrees of freedom, generalizing Wilks' theorem. This provides a fast way to quantify statistical significance in light of the look-elsewhere effect, without resorting to expensive simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Precision redshift-space galaxy power spectra using Zel'dovich control variates

Numerical simulations in cosmology require trade-offs between volume, resolution and run-time that limit the volume of the Universe that can be simulated, leading to sample variance in predictions of ensemble-average quantities such as the power spectrum or correlation function(s). Sample variance is particularly acute at large scales, which is also where analytic techniques can be highly reliable. This provides an opportunity to combine analytic and numerical techniques in a principled way to improve the dynamic range and reliability of predictions for clustering statistics. In this paper we extend the technique of Zel'dovich control variates, previously demonstrated for 2-point functions in real space, to reduce the sample variance in measurements of 2-point statistics of biased tracers in redshift space. We demonstrate that with this technique, we can reduce the sample variance of these statistics down to their shot-noise limit out to k ~ 0.2 h Mpc -1 . This allows a better matching with perturbative models and improved predictions for the clustering of e.g. quasars, galaxies and neutral Hydrogen measured in spectroscopic redshift surveys at very modest computational expense. We discuss the implementation of ZCV, give some examples and provide forecasts for the efficacy of the method under various conditions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Measurement of off-shell Higgs boson production in the $H^*\rightarrow ZZ\rightarrow 4\ell$ decay channel using a neural simulation-based inference technique in 13 TeV pp collisions with the ATLAS detector

A measurement of off-shell Higgs boson production in the $H^*\to ZZ\to 4\ell$ decay channel is presented. The measurement uses 140 fb −1 of proton–proton collisions at $\sqrt{s} = 13$ TeV collected by the ATLAS detector at the Large Hadron Collider and supersedes the previous result in this decay channel using the same dataset. The data analysis is performed using a neural simulation-based inference method, which builds per-event likelihood ratios using neural networks. The observed (expected) off-shell Higgs boson production signal strength in the $ZZ\to 4\ell$ decay channel at 68% CL is $0.87^{+0.75}_{-0.54}$ ($1.00^{+1.04}_{-0.95}$ ). The evidence for off-shell Higgs boson production using the $ZZ\to 4\ell$ decay channel has an observed (expected) significance of 2.5σ (1.3σ). The expected result represents a significant improvement relative to that of the previous analysis of the same dataset, which obtained an expected significance of 0.5σ. When combined with the most recent ATLAS measurement in the $ZZ\to 2\ell 2\nu$ decay channel, the evidence for off-shell Higgs boson production has an observed (expected) significance of 3.7σ (2.4σ). The off-shell measurements are combined with the measurement of on-shell Higgs boson production to obtain constraints on the Higgs boson total width. The observed (expected) value of the Higgs boson width at 68% CL is $4.3^{+2.7}_{-1.9}$ ($4.1^{+3.5}_{-3.4}$ ) MeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Cosmological neutrino mass: a frequentist overview in light of DESI

We derive constraints on the neutrino mass using a variety of recent cosmological datasets, including DESI BAO, the full-shape analysis of the DESI matter power spectrum and the one-dimensional power spectrum of the Lyman-α forest (P1D) from eBOSS quasars as well as the cosmic microwave background (CMB). The constraints are obtained in the frequentist formalism by constructing profile likelihoods and applying the Feldman-Cousins prescription to compute confidence intervals. This method avoids potential prior and volume effects that may arise in a comparable Bayesian analysis. Parabolic fits to the profiles allow one to distinguish changes in the upper limits from variations in the constraining power σ of the different data combinations. We find that all profiles in the ΛCDM model are cut off by the ∑m ν ≥ 0 bound, meaning that the corresponding parabolas reach their minimum in the unphysical sector. The most stringent 95% C.L. upper limit is obtained by the combination of DESI DR2 BAO, Planck PR4 and CMB lensing at 53 meV, below the minimum of 59 meV set by the normal ordering. The corresponding constraining power σ is 43 meV, which highlights the importance of the cut-off by negative values in the determination of the upper limit. Extending ΛCDM to non-zero curvature and w 0 w a CDM relaxes the constraints past 59 meV again, but only w 0 w a CDM exhibits profiles with a minimum at a positive value. Additionally, we extend the formalism to constrain the lightest neutrino mass. For DESI DR2 BAO, Planck PR4 and CMB lensing, we find confidence limits at 20 and 19 meV for normal and inverted ordering, respectively. Using a combination of DESI DR1 full-shape, BBN and eBOSS Lyman-α P1D, we successfully constrain the neutrino mass independently of the CMB. This combination yields m l ≤ 97 and 98 meV in the normal and inverted orderings, and total neutrino mass ∑m ν ≤ 285 meV (95% C.L.). The addition of DESI full-shape or Lyman-α P1D to CMB and DESI BAO results in small but noticeable improvement of the constraining power of the data. Lyman-α free-streaming measurements especially improve the constraint. Since they are based on eBOSS data, this sets a promising precedent for upcoming DESI data.

Frequentist statistics↗
DOE OSTI2026

Frequentist cosmological constraints from full-shape clustering measurements in DESI DR1

We present a frequentist analysis of clustering measurements from Data Release 1 of the Dark Energy Spectroscopic Instrument (DESI) using the standard profile likelihood method. While Bayesian inferences for effective field theory models of galaxy clustering can be highly sensitive to prior choices for extended cosmological models, frequentist inferences are not susceptible to such effects. We compare frequentist and Bayesian constraints for the parameter set {σ 8 , H 0 , Ω m , w 0 , w a } using the full-shape power spectrum multipoles, post-reconstruction baryon acoustic oscillation (BAO) measurements, and external datasets from the CMB and type Ia supernovae measurements. The frequentist confidence intervals are significantly shifted relative to the Bayesian credible intervals for the w 0 w a CDM model, unless supernovae data are included. When DESI full-shape and BAO data are fit jointly, we obtain the following 1σ frequentist confidence intervals for ΛCDM (w 0 w a CDM): σ 8 = 0.863 +0.048 -0.040 , H 0 = 68.96 +0.81 -0.80 km s -1 Mpc -1 , Ω m = 0.3034 ± 0.0110 (σ 8 = 0.782 +0.060 -0.036 , H 0 = 63.7 +4.2 -2.0 km s -1 Mpc -1 , Ω m = 0.378 +0.024 -0.047 , w 0 = -0.16 +0.10 -0.50 , w a = -3.0 +1.7 ), corresponding to 0.8σ, 0.3σ, 0.7σ (2.1σ, 4.1σ, 6.5σ, 6.3σ, 6.6σ) shifts between the maximum likelihood estimate and the Bayesian posterior mean for ΛCDM (w 0 w a CDM) respectively.

Bayesian reasoning↗
DOE OSTI2022

Statistical Significance Testing for Mixed Priors: A Combined Bayesian and Frequentist Analysis

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it incorporates Occam’s razor via the multiplicity or trials factor in the look-elsewhere effect. However, if the prior is not known completely, the frequentist hypothesis test via the false-positive rate is a better approach, as it is less sensitive to the prior choice. We argue that when only partial prior information is available, it is best to combine the two methodologies by using the Bayes factor as a test statistic in the frequentist analysis. We show that the standard frequentist maximum likelihood-ratio test statistic corresponds to the Bayes factor with a non-informative Jeffrey’s prior. We also show that mixed priors increase the statistical power in frequentist analyses over the maximum likelihood test statistic. We develop an analytic formalism that does not require expensive simulations and generalize Wilks’ theorem beyond its usual regime of validity. In specific limits, the formalism reproduces existing expressions, such as the p-value of linear models and periodograms. We apply the formalism to an example of exoplanet transits, where multiplicity can be more than 10 7 . We show that our analytic expressions reproduce the $p$-values derived from numerical simulations. We offer an interpretation of our formalism based on the statistical mechanics. We introduce the counting of states in a continuous parameter space using the uncertainty volume as the quantum of the state. We show that both the $p$-value and Bayes factor can be expressed as an energy versus entropy competition.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Improvement of Drop‐Hammer Impact Testing for Safety Assessment of High Explosives Using 10‐mg Samples

Here, in this study, we established an improved method for drop-hammer impact testing of small quantities of high explosives (10 mg). We performed about seven hundred impact tests under various experimental conditions (e.g., sandpaper vs bare anvil, different sample masses, drop-weights, and striker diameters) to determine an optimal set of conditions and reaction detection methods (e.g., gas analysis, video, and sound recordings) that give the most statistically reliable results with 10 mg samples. We used both Frequentist and Bayesian statistical approaches to compare estimates of the drop height (DH50) that initiates a reaction 50% of the time, and to quantify the associated uncertainty. Gas analysis proved to be the most reliable reaction detection method, showing unambiguous rises in HE decomposition products (e.g., CO 2 ) even when the other indicators (e.g., sound, video) were inconclusive. The impact tests performed with a bare anvil showed much better reproducibility than those conducted with sandpaper, reducing the largest uncertainty observed in the data sets by a factor of 1.7. The DH 50 values obtained from three different sample masses (10, 20, and 35 mg) fell within the uncertainties of the measurements. We demonstrated the improved procedure (i.e., 10-mg samples, gas analysis, bare anvil, and Bayesian approach) on a variety of PETN samples having different surface areas and thermal histories.

PETN↗
DOE OSTI2025

A novel framework for increasing research transparency: Exploring the connection between diversity and innovation

A split sample/dual method research protocol is demonstrated to increase transparency while reducing the probability of false discovery. We apply the protocol to examine whether diversity in ownership teams increases or decreases the likelihood of a firm reporting a novel innovation using data from the 2018 United States Census Bureau’s Annual Business Survey. Transparency is increased in three ways: 1) all specification testing and identifying potentially productive models is done in an exploratory subsample that 2) preserves the validity of hypothesis test statistics fromde novoestimation in the holdout confirmatory sample with 3) all findings publicly documented in an earlier registered report and in this journal publication. Bayesian estimation procedures that leverage information from the exploratory stage included in the confirmatory stage estimation replace traditional frequentist null hypothesis significance testing. In addition to increasing statistical power by using information from the full sample, Bayesian methods directly estimate a probability distribution for the magnitude of an effect, allowing much richer inference. Estimated magnitudes of diversity along academic discipline, race, ethnicity, and foreign-born status dimensions are positively associated with innovation. A maximally diverse ownership team on these dimensions would be roughly six times more likely to report new-to-market innovation than a homophilic team.

Science & Technology - Other Topics↗
DOE OSTI2020

XRD-PUAT (X-Ray Diffraction - Parameter Uncertainty Analysis Toolkit)

This XRD uncertainty toolkit was built to investigate uncertainty and local least squares topology over a specified parameter space on a single histogram in a gpx GSAS-II file. The parameter uncertainty can be investigated using either a frequentist F-test approach or a Bayesian Inference statistical inversion method on a weighted least squares or peak fit refinements.SAND Number: SAND2020-12227 M Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Moore, Alexander↗
DOE OSTI2021

Validation Metrics for Fixed Effects and Mixed-Effects Calibration

The modern scientific process often involves the development of a predictive computational model. To improve its accuracy, a computational model can be calibrated to a set of experimental data. A variety of validation metrics can be used to quantify this process. Some of these metrics have direct physical interpretations and a history of use, while others, especially those for probabilistic data, are more difficult to interpret. In this work, a variety of validation metrics are used to quantify the accuracy of different calibration methods. Frequentist and Bayesian perspectives are used with both fixed effects and mixed-effects statistical models. Through a quantitative comparison of the resulting distributions, the most accurate calibration method can be selected. Two examples are included which compare the results of various validation metrics for different calibration methods. It is quantitatively shown that, in the presence of significant laboratory biases, a fixed effects calibration is significantly less accurate than a mixed-effects calibration. This is because the mixed-effects statistical model better characterizes the underlying parameter distributions than the fixed effects model. The results suggest that validation metrics can be used to select the most accurate calibration model for a particular empirical model with corresponding experimental data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Optimal Cosmic Microwave Background Lensing Reconstruction and Parameter Estimation with SPTpol Data

Here, we perform the first simultaneous Bayesian parameter inference and optimal reconstruction of the gravitational lensing of the cosmic microwave background (CMB), using 100 deg 2 of polarization observations from the SPTpol receiver on the South Pole Telescope. These data reach noise levels as low as 5.8 μK arcmin in polarization, which are low enough that the typically used quadratic estimator (QE) technique for analyzing CMB lensing is significantly suboptimal. Conversely, the Bayesian procedure extracts all lensing information from the data and is optimal at any noise level. We infer the amplitude of the gravitational lensing potential to be ${A}_{\phi }=0.949\,\pm \,0.122$ using the Bayesian pipeline, consistent with our QE pipeline result, but with 17% smaller error bars. The Bayesian analysis also provides a simple way to account for systematic uncertainties, performing a similar job as frequentist "bias hardening" or linear bias correction, and reducing the systematic uncertainty on A Φ due to polarization calibration from almost half of the statistical error to effectively zero. Finally, we jointly constrain A Φ along with A L , the amplitude of lensing-like effects on the CMB power spectra, demonstrating that the Bayesian method can be used to easily infer parameters both from an optimal lensing reconstruction and from the delensed CMB, while exactly accounting for the correlation between the two. These results demonstrate the feasibility of the Bayesian approach on real data, and pave the way for future analysis of deep CMB polarization measurements with SPT-3G, Simons Observatory, and CMB-S4, where improvements relative to the QE can reach 1.5 times tighter constraints on A Φ and seven times lower effective lensing reconstruction noise.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Role of the likelihood for elastic scattering uncertainty quantification

In the last decade, uncertainty quantification (UQ) for optical model potentials (OMPs) has become a focal point for nuclear reaction theory, and several competing approaches for OMP UQ have recently been developed. Here, we clarify recent efforts to compare frequentist and Bayesian approaches in the context of OMP UQ [G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019)]. We replicate a portion of that OMP UQ study but use independent statistical tools. Specifically, we compare two methods for OMP parameter inference from elastic scattering data: the Levenberg-Marquardt algorithm for χ 2 minimization on one hand and Markov chain Monte Carlo (MCMC) sampling on the other. Separately, we assess the common practice of using a renormalized likelihood (χ 2 /N), N being the number of data points, instead of the canonical weighted-least-squares likelihood (χ 2 ), as a way of accounting for unknown data correlations. Here, we show that for a generic linear model and for a five-parameter OMP analysis, frequentist and uniform-prior Bayesian approaches recover the same optimum and uncertainty estimates—not systematically larger uncertainties for the Bayesian approach, as was concluded in G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019). Further, we show that if an additional, near-degenerate parameter is introduced into the same OMP analysis such that the parameter posterior becomes non-Gaussian, then covariance-based estimates of uncertainty become unreliable. Finally, we show that regardless of optimization approach, if χ 2 /N is used for the likelihood, the resulting parametric uncertainties increase by $\sqrt{N}$, and that this is responsible for the conclusions drawn in the revisited study. Based on our replication results, we find that a fortuitous cancellation of unreported errors and the renormalization factor can lead to improvement in empirical coverages, as was the case in the original comparative study. We emphasize that developing and applying a realistic likelihood function is an essential task in a UQ analysis, and that several recent UQ studies that employed a renormalized likelihood (i.e., including a 1/N factor) may have yielded unrealistically large uncertainties for elastic-scattering observables. If the parameter posterior deviates from multivariate-normal, a sampling-based approach like MCMC has a clear advantage over methods that assume the Laplace approximation holds. We note that empirical coverage can serve as an important internal check for the analyst whose model or data may have additional, unaccounted-for uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

MFNets: Multifidelity data-driven networks for Bayesian learning and prediction

This paper presents a multifidelity uncertainty quantification framework called MFNets. We seek to address three existing challenges that arise when experimental and simulation data from different sources are used to enhance statistical estimation and prediction with quantified uncertainty. Specifically, we demonstrate that MFNets can (1) fuse heterogeneous data sources arising from simulations with different parameterizations, e.g simulation models with different uncertain parameters or data sets collected under different environmental conditions; (2) encode known relationships among data sources to reduce data requirements; and (3) improve the robustness of existing multi-fidelity approaches to corrupted data. MFNets construct a network of latent variables (LVs) to facilitate the fusion of data from an ensemble of sources of varying credibility and cost. These LVs are posited as explanatory variables that provide the source of correlation in the observed data. Furthermore, MFNets provide a way to encode prior physical knowledge to enable efficient estimation of statistics and/or construction of surrogates via conditional independence relations on the LVs. We highlight the utility of our framework with a number of theoretical results which assess the quality of the posterior mean as a frequentist estimator and compare it to standard sampling approaches that use single fidelity, multilevel, and control variate Monte Carlo estimators. We also use the proposed framework to derive the Monte Carlo-based control variate estimator entirely from the use of Bayes rule and linear-Gaussian models -- to our knowledge the first such derivation. Finally, we demonstrate the ability to work with different uncertain parameters across different models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Periodicity significance testing with null-signal templates: reassessment of PTF’s SMBH binary candidates

Periodograms are widely employed for identifying periodicity in time series data, yet they often struggle to accurately quantify the statistical significance of detected periodic signals when the data complexity precludes reliable simulations. We develop a data-driven approach to address this challenge by introducing a null-signal template (NST). The NST is created by carefully randomizing the period of each cycle in the periodogram template, rendering it non-periodic. It has the same frequentist properties as a periodic signal template, and we show with simulations that the distribution of false positives is the same as with the original periodic template, regardless of the underlying data. Thus, performing a periodicity search with the NST acts as an effective simulation of the null (no-signal) hypothesis, without having to simulate the noise properties of the data. We apply the NST method to the supermassive black hole binaries (SMBHB) search in the Palomar Transient Factory (PTF), where Charisi et al. had previously proposed 33 high signal-to-noise candidates utilizing simulations to quantify their significance. Our approach reveals that these simulations do not capture the complexity of the real data. There are no statistically significant periodic signal detections above the non-periodic background. To improve the search sensitivity, we introduce a Gaussian quadrature based algorithm for the Bayes Factor with correlated noise as a test statistic. We show with simulations that this improves sensitivity to true signals by more than an order of magnitude. However, the Bayes Factor approach also results in no statistically significant detections in the PTF data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Probing the consistency of cosmological contours for supernova cosmology

As the scale of cosmological surveys increases, so does the complexity in the analyses. This complexity can often make it difficult to derive the underlying principles, necessitating statistically rigorous testing to ensure the results of an analysis are consistent and reasonable. This is particularly important in multi-probe cosmological analyses like those used in the Dark Energy Survey (DES) and the upcoming Legacy Survey of Space and Time, where accurate uncertainties are vital. In this paper, we present a statistically rigorous method to test the consistency of contours produced in these analyses and apply this method to the Pippin cosmological pipeline used for type Ia supernova cosmology with the DES. We make use of the Neyman construction, a frequentist methodology that leverages extensive simulations to calculate confidence intervals, to perform this consistency check. A true Neyman construction is too computationally expensive for supernova cosmology, so we develop a method for approximating a Neyman construction with far fewer simulations. We find that for a simulated dataset, the 68% contour reported by the Pippin pipeline and the 68% confidence region produced by our approximate Neyman construction differ by less than a percent near the input cosmology; however, they show more significant differences far from the input cosmology, with a maximal difference of 0.05 in $Ω$ M and 0.07 in w. In conclusion, this divergence is most impactful for analyses of cosmological tensions, but its impact is mitigated when combining supernovae with other cross-cutting cosmological probes, such as the cosmic microwave background.

79 ASTRONOMY AND ASTROPHYSICS↗