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Results for “BAYESIAN STATISTICS”

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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Applications of Bayesian Statistics to Problems in Gamma-Ray Bursts

This presentation will describe two applications of Bayesian statistics to Gamma Ray Bursts (GRBS). The first attempts to quantify the evidence for a cosmological versus galactic origin of GRBs using only the observations of the dipole and quadrupole moments of the angular distribution of bursts. The cosmological hypothesis predicts isotropy, while the galactic hypothesis is assumed to produce a uniform probability distribution over positive values for these moments. The observed isotropic distribution indicates that the Bayes factor for the cosmological hypothesis over the galactic hypothesis is about 300. Another application of Bayesian statistics is in the estimation of chance associations of optical counterparts with galaxies. The Bayesian approach is preferred to frequentist techniques here because the Bayesian approach easily accounts for galaxy mass distributions and because one can incorporate three disjoint hypotheses: (1) bursts come from galactic centers, (2) bursts come from galaxies in proportion to luminosity, and (3) bursts do not come from external galaxies. This technique was used in the analysis of the optical counterpart to GRB970228.

Meegan, Charles A.↗
NASA NTRS2020

Bayesian Statistical Models for Community Annoyance Survey Data

This paper demonstrates the use of two Bayesian statistical models to analyze single-event sonic boom exposure and human annoyance data from community response surveys. Each model is fit to data from a NASA pilot study.Unlike many community noise surveys, this study used a panel sample to collect multiple observations per participant instead of a single observation. Thus, a multilevel (also known as hierarchical or mixed-effects) model is used to account for the within-subject correlation in the panel sample data. This paper describes a multilevel logistic regression model and a multilevel ordinal regression model. The paper also proposes a method for calculating a summary dose-response curve from the multilevel models that represents the population. The two models’ summary dose-response curves are visually similar. However, their estimates differ when calculating the noise dose at a fixed percent highly annoyed.

Musical instruments↗
NASA NTRS2015

Online Dectection and Modeling of Safety Boundaries for Aerospace Application Using Bayesian Statistics

The behavior of complex aerospace systems is governed by numerous parameters. For safety analysis it is important to understand how the system behaves with respect to these parameter values. In particular, understanding the boundaries between safe and unsafe regions is of major importance. In this paper, we describe a hierarchical Bayesian statistical modeling approach for the online detection and characterization of such boundaries. Our method for classification with active learning uses a particle filter-based model and a boundary-aware metric for best performance. From a library of candidate shapes incorporated with domain expert knowledge, the location and parameters of the boundaries are estimated using advanced Bayesian modeling techniques. The results of our boundary analysis are then provided in a form understandable by the domain expert. We illustrate our approach using a simulation model of a NASA neuro-adaptive flight control system, as well as a system for the detection of separation violations in the terminal airspace.

Statistics↗
NASA NTRSDate not supplied

A Framework for Software Health Management Using Bayesian Statistics

Software Health Management (SWHM) must make sure that the software always remains in safe and healthy regions of the state space. Boundaries between healthy and unhealthy regions are important for the detection of violations and health management.In this position paper, we present a framework, which employs techniques from Bayesian statistical modeling and active learning to efficiently characterize health boundaries in high-dimensional spaces. We will discuss, how this framework supports SWHM during design time and during operation of learning/adapting software systems

software health management↗
NASA NTRS2014

Bayesian Statistics and Uncertainty Quantification for Safety Boundary Analysis in Complex Systems

The analysis of a safety-critical system often requires detailed knowledge of safe regions and their highdimensional non-linear boundaries. We present a statistical approach to iteratively detect and characterize the boundaries, which are provided as parameterized shape candidates. Using methods from uncertainty quantification and active learning, we incrementally construct a statistical model from only few simulation runs and obtain statistically sound estimates of the shape parameters for safety boundaries.

Active Learning↗
NASA NTRS2004

Neural network uncertainty assessment using Bayesian statistics: a remote sensing application

Neural network (NN) techniques have proved successful for many regression problems, in particular for remote sensing; however, uncertainty estimates are rarely provided. In this article, a Bayesian technique to evaluate uncertainties of the NN parameters (i.e., synaptic weights) is first presented. In contrast to more traditional approaches based on point estimation of the NN weights, we assess uncertainties on such estimates to monitor the robustness of the NN model. These theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature, microwave surface emissivities, and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land. The weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs (i.e., error bars and correlation structure of these errors). Such quantities are very important for evaluating any application of an NN model. The uncertainties on the NN Jacobians are then considered in the third part of this article. Used for regression fitting, NN models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis is put on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the regression model. The complex structure of dependency inside the NN is the essence of the model, and assessing its quality, coherency, and physical character makes all the difference between a blackbox model with small output errors and a reliable, robust, and physically coherent model. Such dependency structures are described to the first order by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model for given input data. We use a Monte Carlo integration procedure to estimate the robustness of the NN Jacobians. A regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these Jacobians robust and physically meaningful.

Neural Networks (Computer)↗
DOE OSTI2025

Bayesian Statistical Analysis for Mass Spectrometric Data Processing

• Thermal ionization mass spectrometry (TIMS) is a “gold standard’ technique for actinide isotope amount ratio and assay measurements. • Ubiquitously used in: • Nuclear Nonproliferation • Nuclear Safeguards • Nuclear Forensics • Basic Science • Savannah River National Laboratory (SRNL) installed a new Thermo Scientific TRITON Plus TIMS in early 2024.

McLarty, Ellis C. [Savannah River National Laborat↗
DOE OSTI2025

Bayesian Statistical Analysis for Mass Spectrometric Data Processing

Thermal ionization mass spectrometry (TIMS) is a “gold standard’ technique for actinide isotope amount ratio and assay measurements. • Ubiquitously used in: • Nuclear Nonproliferation • Nuclear Safeguards • Nuclear Forensics • Basic Science • Savannah River National Laboratory (SRNL) installed a new Thermo Scientific TRITON Plus TIMS in early 2024.

McLarty, Ellis C. [Savannah River National Laborat↗
NASA NTRSDate not supplied

A Framework for the Analysis of Deep Neural Networks in Autonomous Aerospace Applications using Bayesian Statistics

Deep Neural Networks (DNNs) are considered to be key components in many autonomous systems. Applications range from vision-based obstacle avoidance to intelligent/learning control and planning. Safety-critical applications as found in the aerospace domain require that the behavior of the DNN is validated and tested rigorously for safety of the autonomous system (AUS). In this paper, we present a framework to support testing of DNNs and the analysis of the network structure. Our framework employs techniques from statistical modeling and active learning to effectively generate test cases for DNN safety testing and performance analysis. We will present results of a case study on a physics-based Deep recurrent residual neural network (DR-RNN), which has been trained to emulate the aerodynamics behavior of a fixed-wing aircraft.

Deep Neural networks↗
NASA NTRS2006

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted

Pohorille, Andrew↗
NASA NTRS1993

A new technique for deconvolution of data from instruments that make integral measurements, e.g. RIMS on DE-1

A general method for deconvolving an unknown function from integral measurements is described and applied to data from the instrument Retarding Ion Mass Spectrometer (RIMS) aboard the spacecraft Dynamics Explorer 1 (DE-1). The principal features of the method are: (1) it uses objective criteria based upon fundamental statistical principles, i.e. Bayesian statistics; (2) it provides for insertion of prior knowledge in a non-prejudicial, explicit manner through the choice of breakpoints that determine the bicubic spline expansion functions; (3) it prevents random fluctuations from controlling the fit to the data through the use of singular value decomposition and the elimination of small singular values; and (4) it guards agianst the introduction of spurious features into the result by including a penalty function and using the principle of generalized cross validation. Illustrative examples from RIMS data for H(+) and O(+) show that the method provides enhanced accuracy and detail in deconvolving the ion phase space density.

Perez, J. D.↗
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

Hot Droughts and Forest Tree Dynamics in the Amazon - Statistical Models, Scripts, Data, and Outputs

This package contains data, outputs, equations, and R scripts for analyses for manuscript entitled "Hot droughts in the Amazon: A window to a future hypertropical climate" by J. Chambers et al., in particular it contains statistical models and analyses for the INPA BIONTE tree mortality study. The Models folder contains details for all statistical models in PDF files. The Scripts folder contains the R scripts for Bayesian Hierarchical Models (two text files) and SEMs (one text file) are separate and reasonably annotated. All data associated with these scripts are in the data folder. The Data folder contains two of the three CSV files used for the analyses and are called by the R scripts. Two of them are part of published datasets (`BIONTE_mortality-rates.csv` from Lima et al. 2024, DOI:10.15486/ngt/1898910 and `SPEI.csv` from Pastorello et al. 2023 DOI:10.15486/ngt/1958257) and also provided in this package for convenience (please see the corresponding datasets for usage and citation terms). The third dataset (`BIONTE_gapfilled_wd.csv`) contains sensitive information and can be obtained by contacting the manuscript lead author. The Outputs folder contains the two output files that provide extra information about the analyses. The file `figuresFeb2025d.pdf` contains all the figures from the manuscript - captions are in the manuscript. The file `ChambersMS.pdf` contains primary results from Bayesian statistical models, regression analyses, and validation steps applied to the tree mortality data from the INPA experiments. The document includes visual summaries, model diagnostics, and leave-one-out (LOO) validation results. A breakdown of file contents can be found in the README file that is part of this package.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1989

A Bayesian approach to reliability and confidence

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

Barnes, Ron↗
NASA 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↗