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Results for “Likelihood Functions”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Mobile sensing of point-source gas emissions using Bayesian inference: An empirical examination of the likelihood function

This paper evaluates likelihood function forms for Bayesian inference of point-source gas emissions using a mobile sensor. Whereas Bayesian inference has been successfully used to estimate emission rates from time-averaged concentration data measured by stationary sensors, data collected by mobile sensors do not represent ensemble or time-averaged conditions. To examine the potential impact of this contrast, controlled release experiments were conducted with a mobile sensor measuring concentrations repeatedly along transverse cross sections of the downwind plumes. Experiments were conducted with measurements made at different downwind distances, different sensor heights, and with different obstacle states. An examination is made between two commonly-used likelihood functions, the Gaussian and the log-normal. For experiments conducted in the absence of obstacles, the Bayesian estimates using the log-normal likelihood function yield a much smaller bias than those based on the Gaussian likelihood function. This finding is consistent with the non-Gaussian nature of concentration fluctuations near a point-source. For experiments conducted in the presence of obstacles, the Bayesian inference based on the Gaussian likelihood function exhibits a better performance. This can be explained by the enhanced turbulent mixing due to the obstacle-introduced wake eddies. Overall, we find that the selection of the likelihood function can be physically related to the underlying conditions, and the proper selection is critical to ensure the performance of the Bayesian inference for source characterization using mobile sensing data.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Evaluating crystallographic likelihood functions using numerical quadratures

Intensity-based likelihood functions in crystallographic applications have the potential to enhance the quality of structures derived from marginal diffraction data. Their usage, however, is complicated by the ability to efficiently compute these target functions. Here, a numerical quadrature is developed that allows the rapid evaluation of intensity-based likelihood functions in crystallographic applications. By using a sequence of change-of-variable transformations, including a nonlinear domain-compression operation, an accurate, robust and efficient quadrature is constructed. The approach is flexible and can incorporate different noise models with relative ease.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Improved renormalization group computation of likelihood functions for cosmological data sets

Evaluation of likelihood functions for cosmological large scale structure data sets (including CMB, galaxy redshift surveys, etc.) naturally involves marginalization, i.e., integration, over an unknown underlying random signal field. Recently, I showed how a renormalization group method can be used to carry out this integration efficiently by first integrating out the smallest scale structure, i.e., localized structure on the scale of differences between nearby data cells, then combining adjacent cells in a coarse graining step, then repeating this process over and over until all scales have been integrated. Here I extend the formulation in several ways in order to reduce the prefactor on the method's linear scaling with data set size. The key improvement is showing how to integrate out the difference between specific adjacent cells before summing them in the coarse graining step, compared to the original formulation in which small-scale fluctuations were integrated more generally. I suggest some other improvements in details of the scheme, including showing how to perform the integration around a maximum likelihood estimate for the underlying random field. In the end, an accurate likelihood computation for a million-cell Gaussian test data set runs in two minutes on my laptop, with room for further optimization and straightforward parallelization.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Renormalization group computation of likelihood functions for cosmological data sets

I show how a renormalization group (RG) method can be used to incrementally integrate the information in cosmological large-scale structure data sets (including CMB, galaxy redshift surveys, etc.). I show numerical tests for Gaussian fields, where the method allows arbitrarily close to exact computation of the likelihood function in order N time, even for problems with no symmetry, compared to N 3 for brute force linear algebra (where N is the number of data points - to be fair, methods already exist to solve the Gaussian problem in at worst N log N time, and this method will not necessarily be faster in practice). The method requires no sampling or other Monte Carlo (random) element. Nonlinearity/non-Gaussianity can be accounted for to the extent that terms generated by integrating out small scale modes can be projected onto a sufficient basis, e.g., at least in the sufficiently perturbative regime. The formulas to evaluate are straightforward and require no understanding of quantum field theory, but this paper may also serve as a pedagogical introduction to Wilsonian RG for astronomers.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Non-Gaussianity in the weak lensing correlation function likelihood – implications for cosmological parameter biases

ABSTRACT We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in 1D marginal distributions of shear two-point correlation functions in simulated weak lensing data. We examine the implications in the context of future surveys, in particular LSST, with derivations of how the non-Gaussianity scales with survey area. We show that there is no significant bias in 1D posteriors of Ωm and σ8 due to the non-Gaussian likelihood distributions of shear correlations functions using the mock data (100 deg2). We also present a systematic approach to constructing approximate multivariate likelihoods with 1D parametric functions by assuming independence or more flexible non-parametric multivariate methods after decorrelating the data points using principal component analysis (PCA). While the use of PCA does not modify the non-Gaussianity of the multivariate likelihood, we find empirically that the 1D marginal sampling distributions of the PCA components exhibit less skewness and kurtosis than the original shear correlation functions. Modelling the likelihood with marginal parametric functions based on the assumption of independence between PCA components thus gives a lower limit for the biases. We further demonstrate that the difference in cosmological parameter constraints between the multivariate Gaussian likelihood model and more complex non-Gaussian likelihood models would be even smaller for an LSST-like survey. In addition, the PCA approach automatically serves as a data compression method, enabling the retention of the majority of the cosmological information while reducing the dimensionality of the data vector by a factor of ∼5.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Dwarf spheroidal J-factor likelihoods for generalized NFW profiles

ABSTRACT Indirect detection strategies of particle dark matter (DM) in Dwarf spheroidal satellite galaxies (dSphs) typically entail searching for annihilation signals above the astrophysical background. To robustly compare model predictions with the observed fluxes of product particles, most analyses of astrophysical data – which are generally frequentist – rely on estimating the abundance of DM by calculating the so-called J factor. This quantity is usually inferred from the kinematic properties of the stellar population of a dSph using the Jeans equation, commonly by means of Bayesian techniques that entail the presence (and additional systematic uncertainty) of prior choice. Here, extending earlier work, we develop a scheme to derive the profile likelihood for J factors of dwarf spheroidals for models with five or more free parameters. We validate our method on a publicly available simulation suite, released by the Gaia Challenge, finding satisfactory statistical properties for bias and probability coverage. We present the profile likelihood function and maximum likelihood estimates for the J-factor of 10 dSphs. As an illustration, we apply these profile likelihoods to recently published analyses of γ-ray data with the Fermi Large Area Telescope to derive new, consistent upper limits on the DM annihilation cross-section. We do this for a subset of systems, generally referred to as classical dwarfs. The implications of these findings for DM searches are discussed, together with future improvements and extensions of this technique.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Bayesian optimization of generalized data

Direct application of Bayes' theorem to generalized data yields a posterior probability distribution function (PDF) that is a product of a prior PDF of generalized data and a likelihood function, where generalized data consists of model parameters, measured data, and model defect data. The prior PDF of generalized data is defined by prior expectation values and a prior covariance matrix of generalized data that naturally includes covariance between any two components of generalized data. A set of constraints imposed on the posterior expectation values and covariances of generalized data via a given model is formally solved by the method of Lagrange multipliers. Posterior expectation values of the constraints and their covariance matrix are conventionally set to zero, leading to a likelihood function that is a Dirac delta function of the constraining equation. It is shown that setting constraints to values other than zero is analogous to introducing a model defect. Since posterior expectation values of any function of generalized data are integrals of that function over all generalized data weighted by the posterior PDF, all elements of generalized data may be viewed as nuisance parameters marginalized by this integration. One simple form of posterior PDF is obtained when the prior PDF and the likelihood function are normal PDFs. For linear models without a defect this PDF becomes equivalent to constrained least squares (CLS) method, that is, the χ2 minimization method.

Arbanas, Goran↗
DOE OSTI2025

ASCR Workshop Position Paper: Challenges and Opportunities in High Energy Physics

High energy particle physics and cosmology concern themselves with estimating fundamental parameters of nature, such as the masses and interactions of fundamental particles like the Higgs boson and the rate of expansion of the universe. In doing so, they analyze exabyte-scale datasets, some of the largest in all of science, and face many challenges in subsequent data analysis. These challenges are shared between the two disciplines, but we focus on particle physics to highlight one specific domain. In particle physics, the standard method for estimating parameters involves performing Monte Carlo (MC) integration as a function of both parameters of interest and nuisance parameters using an expensive simulator, counting the number of observed collision events (i.i.d. samples) from an experiment in the corresponding integration domains, and forming a Poisson likelihood function. This likelihood function is then used in a Frequentist manner to construct a maximum likelihood point estimate (MLE) and confidence set for the parameters. To sufficiently populate the high-dimensional integration domains, simulators consume billions of CPU-hours annually and produce hundreds of petabytes of intermediate output data. Several techniques have been developed to: optimize definitions of the integration domains so as to be maximally sensitive to a particular subset of parameters, efficiently estimate the integrals, and build robust surrogate models by interpolating between integral evaluations at different parameter points. One can view this whole endeavor as classical Simulation-Based Inference (SBI).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Data-driven delta-generalized labeled multi-bernoulli tracker

A system and method for tracking a plurality of objects. Unlabeled measurement data identifying a plurality of targets corresponding to the plurality of objects is received. A multi-target likelihood function is generated using a persistent target density, a birth target density, and a clutter density. The multi-target likelihood function is used to associate persistent targets with the unlabeled measurement data to update persistent tracks and to initiate a new track for each target in the plurality of targets in the measurement data that is not associated with a persistent target.

LeGrand, Keith Allen↗
DOE OSTI2022

Multi-variance replica exchange SGMCMC for inverse and forward problems via Bayesian PINN

Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging because of the non-convex loss functions and the multiple optima in the Bayesian inverse problem. In this work, we propose a multi-variance replica exchange stochastic gradient Langevin dynamics method to tackle the challenge of the multiple local optima in the optimization and the challenge of the multiple modal posterior distribution in the inverse problem. Replica exchange methods are capable of escaping from the local traps and accelerating the convergence; two chains with different temperatures are designed where the low temperature chain aims for the local convergence, and the target of the high temperature chain is to travel globally and explore the whole loss function entropy landscape. However, it may not be efficient to solve mathematical inversion problems by using the vanilla replica method directly since the method doubles the computational cost in evaluating the forward solvers (likelihood functions) in the two chains. To address this issue, we propose to make different assumptions on the energy function estimation and this facilities one to use solvers of different fidelities in the likelihood function evaluation. More precisely, one can use a solver with low fidelity in the high temperature chain while using a solver with high fidelity in the low temperature chain. Our proposed method significantly lowers the computational cost in the high temperature chain, meanwhile preserving the accuracy and converging very fast. Here we give an unbiased estimate of the swapping rate and give an estimation of the discretization error of the scheme. To verify our idea, we design and solve four inverse problems which have multiple modes. The proposed method is also employed to train the Bayesian PINN to solve the forward and inverse problems; faster and more accurate convergence has been observed when compared to the stochastic gradient Langevin dynamics (SGLD) method and vanilla replica exchange methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A NICER View of the Massive Pulsar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy

We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740+6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint North American Nanohertz Observatory for Gravitational Waves and Canadian Hydrogen Intensity Mapping Experiment/Pulsar wideband radio timing measurements of Fonseca et al. We use XMM-Newton European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740+6620 to be ${12.39}_{-0.98}^{+1.30}$ km and ${2.072}_{-0.066}^{+0.067}$ M ⊙ respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, conditional on surface hot regions that are non-overlapping spherical caps of fully ionized hydrogen atmosphere with uniform effective temperature; a posteriori, the temperature is ${\mathrm{log}}_{10}(T\,[{\rm{K}}])={5.99}_{-0.06}^{+0.05}$ for each hot region. All software for the X-ray modeling framework is open-source and all data, model, and sample information is publicly available, including analysis notebooks and model modules in the Python language. Furthermore, our marginal likelihood function of mass and equatorial radius is proportional to the marginal joint posterior density of those parameters (within the prior support) and can thus be computed from the posterior samples.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Statistically Rigorous Uncertainty Quantification for Physical Parameter Model Calibration with Functional Output

In experiments conducted on the Z-machine at Sandia National Laboratories, dynamic material properties cannot be analyzed using traditional analytic methods, necessitating solving an inverse problem. Bayesian model calibration is a statistical framework for solving an inverse problem to estimate parameters input into a computational model in the presence of multiple uncertainties. Disentangling input parameter uncertainty and model misspecification is often poorly identified problem. When using computational models for physical parameter estimation, the issue of parameter identifiability must be carefully considered to obtain accurate and precise estimates of physical parameters. Additionally, in dynamic material properties applications, the experimental output is a function, velocity over time. While we can sample an arbitrarily large number of points from the measured velocity, these curves only contain a finite amount of information about the calibration parameters. In this report, we propose modifications to the Bayesian model calibration framework to simplify and improve the estimation of physical parameters with functional outputs. Specifically, we propose scaling the likelihood function by an effective sample size rather than modeling the discrepancy function; and modularizing input nuisance parameters with weakly identified parameters. We evaluate the performance of these proposed methods using a statistical simulation study and then apply these methods to estimate parameters of the tantalum equation of state. We conclude that these proposed methods can provide simple, fast, and statistically valid alternatives to the full Bayesian model calibration procedure; and that these methods can be used to estimate parameters of the equation of state for tantalum.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Deep probabilistic direction prediction in 3D with applications to directional dark matter detectors

Abstract We present the first method to probabilistically predict 3D direction in a deep neural network model. The probabilistic predictions are modeled as a heteroscedastic von Mises-Fisher distribution on the sphere S 2 , giving a simple way to quantify aleatoric uncertainty. This approach generalizes the cosine distance loss which is a special case of our loss function when the uncertainty is assumed to be uniform across samples. We develop approximations required to make the likelihood function and gradient calculations stable. The method is applied to the task of predicting the 3D directions of electrons, the most complex signal in a class of experimental particle physics detectors designed to demonstrate the particle nature of dark matter and study solar neutrinos. Using simulated Monte Carlo data, the initial direction of recoiling electrons is inferred from their tortuous trajectories, as captured by the 3D detectors. For 40 keV electrons in a 70% He 30% CO 2 gas mixture at STP, the new approach achieves a mean cosine distance of 0.104 (26 ∘ ) compared to 0.556 (64 ∘ ) achieved by a non-machine learning algorithm. We show that the model is well-calibrated and accuracy can be increased further by removing samples with high predicted uncertainty. This advancement in probabilistic 3D directional learning could increase the sensitivity of directional dark matter detectors.

Computer Science↗
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 OSTI2021

Analysis and Optimization of Seismo-Acoustic Monitoring Networks with Bayesian Optimal Experimental Design

The Bayesian optimal experimental design (OED) problem seeks to identify data, sensor configurations, or experiments which can optimally reduce uncertainty. The goal of OED is to find an experiment that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge about expected data. Therefore, within the context of seismic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types, and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize the ability to locate seismic events from arrival time data of detected seismic phases. In order to do utilize Bayesian OED we must develop four elements:1. A likelihood function that describes the uncertainty of detection and travel times; 2. A Bayesian solver that takes a prior and likelihood to identify the posterior; 3. An algorithm to compute EIG; and, 4. An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we can explore many relevant questions to monitoring such as: how and what multiphenomenology data can be used to optimally reduce uncertainty, how to trade off sensor fidelity and earth model uncertainty, and how sensor types, number, and locations influence uncertainty

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

A flexible event reconstruction based on machine learning and likelihood principles

Event reconstruction is a central step in many particle physics experiments, turning detector observables into parameter estimates; for example estimating the energy of an interaction given the sensor readout of a detector. A corresponding likelihood function is often intractable, and approximations need to be constructed. Here, in our work, we first show how the full likelihood for a many-sensor detector can be broken apart into smaller terms, and secondly how we can train neural networks to approximate all terms solely based on forward simulation. Our technique results in a fast, flexible, and close-to-optimal surrogate model proportional to the likelihood and can be used in conjunction with standard inference techniques allowing for a consistent treatment of uncertainties. We illustrate our technique for parameter inference in neutrino telescopes based on maximum likelihood and Bayesian posterior sampling. Given its great flexibility, we also showcase our method for geometry optimization enabling to learn optimal detector designs. Lastly, we apply our method to realistic simulation of a ton-scale water-based liquid scintillator detector.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗