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DOE OSTI2018

Adverse Event Prediction Using Graph-Augmented Temporal Analysis (Final Report)

This report summarizes the work performed under the Sandia LDRD project "Adverse Event Prediction Using Graph-Augmented Temporal Analysis." The goal of the project was to develop a method for analyzing multiple time-series data streams to identify precursors providing advance warning of the potential occurrence of events of interest. The proposed approach combined temporal analysis of each data stream with reasoning about relationships between data streams using a geospatial-temporal semantic graph. This class of problems is relevant to several important topics of national interest. In the course of this work we developed new temporal analysis techniques, including temporal analysis using Markov Chain Monte Carlo techniques, temporal shift algorithms to refine forecasts, and a version of Ripley's K-function extended to support temporal precursor identification. This report summarizes the project's major accomplishments, and gathers the abstracts and references for the publication submissions and reports that were prepared as part of this work. We then describe work in progress that is not yet ready for publication.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Adverse Event Prediction Using Graph-Augmented Temporal Analysis (Final Report)

This report summarizes the work performed under the Sandia LDRD project "Adverse Event Prediction Using Graph-Augmented Temporal Analysis." The goal of the project was to develop a method for analyzing multiple time-series data streams to identify precursors providing advance warning of the potential occurrence of events of interest. The proposed approach combined temporal analysis of each data stream with reasoning about relationships between data streams using a geospatial-temporal semantic graph. This class of problems is relevant to several important topics of national interest. In the course of this work we developed new temporal analysis techniques, including temporal analysis using Markov Chain Monte Carlo techniques, temporal shift algorithms to refine forecasts, and a version of Ripley's K-function extended to support temporal precursor identification. This report summarizes the project's major accomplishments, and gathers the abstracts and references for the publication sub-missions and reports that were prepared as part of this work. We then describe work in progress that is not yet ready for publication.

42 ENGINEERING↗

DOE OSTI2022

Six Machine-Learning Methods for Predicting Hospital-Stay Duration for Patients with Sepsis: A Comparative Study

Sepsis is a life-threatening medical condition that, if not treated promptly, can result in tissue damage, organ failure, and death. According to the Centers for Disease Control, about 270,000 individuals die of sepsis in the US each year. Further, sepsis expenditures accounted for 13% of total US hospital costs in 2013, totaling more than $24 billion. Our project objectives were to determine if Machine Learning algorithms could reliably predict hospital stay duration for patients with sepsis. The data set we used has been de-identified and is freely available through the BupaR package. The data includes 1050 cases, 15214 events, and 16 types of actions related to sepsis patient care. First, we used process mining to determine how long each patient was in the hospital. Using BupaR’s functions, we created several process model graphs. These process models depict the movement of patients at a hospital and provide duration data for each patent case. Second, we identified outlier data and created two dataset versions: one with and one without outliers. We then applied the following analysis methods: Linear Regression, Random Forest, K-Nearest Neighbors, Neural Networks, XGBoost, and lightGBM. We compared the model validations for the six machine learning models using the same data-splitting method. We found that the XGBoost model had the best prediction accuracy of 73.9 percent for cases with outliers, and 79 percent for cases without outliers. We also found that the lightGBM model had the lowest mean absolute error between prediction and actual duration in days with 3.66 days for the case with outliers, and 2.4 days for the case without outliers. These two models outperformed the other four models. This work will be enhanced in the future by exploring new prediction algorithms and comparing them with the results of this study.

Chen, Lingtao↗

DOE OSTI2020

A review of methods for the reconstruction and analysis of integrated genome-scale models of metabolism and regulation

The current survey aims to describe the main methodologies for extending the reconstruction and analysis of genome-scale metabolic models and phenotype simulation with Flux Balance Analysis mathematical frameworks, via the integration of Transcriptional Regulatory Networks and/or gene expression data. Although the surveyed methods are aimed at improving phenotype simulations obtained from these models, the perspective of reconstructing integrated genome-scale models of metabolism and gene expression for diverse prokaryotes is still an open challenge.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2015

In-situ Condition Monitoring of Components in Small Modular Reactors Using Process and Electrical Signature Analysis. Final report, volume 1. Development of experimental flow control loop, data analysis and plant monitoring

The research and development under this project was focused on the following three major objectives: Objective 1: Identification of critical in-vessel SMR components for remote monitoring and development of their low-order dynamic models, along with a simulation model of an integral pressurized water reactor (iPWR). Objective 2: Development of an experimental flow control loop with motor-driven valves and pumps, incorporating data acquisition and on-line monitoring interface. Objective 3: Development of stationary and transient signal processing methods for electrical signatures, machinery vibration, and for characterizing process variables for equipment monitoring. This objective includes the development of a data analysis toolbox. The following is a summary of the technical accomplishments under this project: - A detailed literature review of various SMR types and electrical signature analysis of motor-driven systems was completed. A bibliography of literature is provided at the end of this report. Assistance was provided by ORNL in identifying some key references. - A review of literature on pump-motor modeling and digital signal processing methods was performed. - An existing flow control loop was upgraded with new instrumentation, data acquisition hardware and software. The upgrading of the experimental loop included the installation of a new submersible pump driven by a three-phase induction motor. All the sensors were calibrated before full-scale experimental runs were performed. - MATLAB-Simulink model of a three-phase induction motor and pump system was completed. The model was used to simulate normal operation and fault conditions in the motor-pump system, and to identify changes in the electrical signatures. - A simulation model of an integral PWR (iPWR) was updated and the MATLAB-Simulink model was validated for known transients. The pump-motor model was interfaced with the iPWR model for testing the impact of primary flow perturbations (upsets) on plant parameters and the pump electrical signatures. Additionally, the reactor simulation is being used to generate normal operation data and data with instrumentation faults and process anomalies. A frequency controller was interfaced with the motor power supply in order to vary the electrical supply frequency. The experimental flow control loop was used to generate operational data under varying motor performance characteristics. Coolant leakage events were simulated by varying the bypass loop flow rate. The accuracy of motor power calculation was improved by incorporating the power factor, computed from motor current and voltage in each phase of the induction motor.- A variety of experimental runs were made for steady-state and transient pump operating conditions. Process, vibration, and electrical signatures were measured using a submersible pump with variable supply frequency. High correlation was seen between motor current and pump discharge pressure signal; similar high correlation was exhibited between pump motor power and flow rate. Wide-band analysis indicated high coherence (in the frequency domain) between motor current and vibration signals. - Wide-band operational data from a PWR were acquired from AMS Corporation and used to develop time-series models, and to estimate signal spectrum and sensor time constant. All the data were from different pressure transmitters in the system, including primary and secondary loops. These signals were pre-processed using the wavelet transform for filtering both low-frequency and high-frequency bands. This technique of signal pre-processing provides minimum distortion of the data, and results in a more optimal estimation of time constants of plant sensors using time-series modeling techniques.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

New method for level-lifetime measurements with thick scintillators

Level lifetimes provide key insight into the structure of atomic nuclei and serve as stringent tests of theoretical descriptions. Though several methods for determining level lifetimes exist for both reaction measurements and decay studies, here the focus is on techniques involving the direct measurement of time differences between population and subsequent depopulation of excited states. The techniques presented herein are broadly applicable across multiple timing ranges, but the approach is specifically described for the βγ timing method. A multi-step, amplitude-dependent time walk correction was employed to address the data analysis complications that arise from using thick scintillators for electron detection. Further, additional corrections for the depth of the interaction must also be performed when the parent isotope has been implanted into the detector. Techniques are presented for performing these time walk and depth of interaction corrections. Subsequently, a new Monte Carlo method utilizing measured detector responses obtained from the data, coupled with chi-square minimization, is presented for extracting excited state lifetimes ≳ 100 picoseconds. The framework of this Monte Carlo method is developed for the decay of a state in 68 Zn with a known 1.6 ps half life, which is considered prompt given the detection sensitivity of the technique, and then benchmarked using two other excited states in neutron-rich Ni isotopes with 120(34) ps and 1.05(3) ns half lives. Using this new method which takes into account the thick scintillator used, these same half lives were measured to be 135(10) ps and 1.04(24) ns, respectively. The overall good agreement demonstrates the validity of the technique.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2013

Life Cycle Analysis Data and Results for Geothermal and Other Electricity Generation Technologies

Life cycle analysis (LCA) is an environmental assessment method that quantifies the environmental performance of a product system over its entire lifetime, from cradle to grave. Based on a set of relevant metrics, the method is aptly suited for comparing the environmental performance of competing products systems. This file contains LCA data and results for electric power production including geothermal power. The LCA for electric power has been broken down into two life cycle stages, namely plant and fuel cycles. Relevant metrics include the energy ratio and greenhouse gas (GHG) ratios, where the former is the ratio of system input energy to total lifetime electrical energy out and the latter is the ratio of the sum of all incurred greenhouse gases (in CO2 equivalents) divided by the same energy output. Specific information included herein are material to power (MPR) ratios for a range of power technologies for conventional thermoelectric, renewables (including three geothermal power technologies), and coproduced natural gas/geothermal power. For the geothermal power scenarios, the MPRs include the casing, cement, diesel, and water requirements for drilling wells and topside piping. Also included herein are energy and GHG ratios for plant and fuel cycle stages for the range of considered electricity generating technologies. Some of this information are MPR data extracted directly from the literature or from models (eg. ICARUS - a subset of ASPEN models) and others (energy and GHG ratios) are results calculated using GREET models and MPR data. MPR data for wells included herein were based on the Argonne well materials model and GETEM well count results.

15 GEOTHERMAL ENERGY↗

DOE OSTI2024

Carbon fiber classification using raman spectroscopy

Carbon fiber characterization processes are described that include multi-condition Raman spectroscopy-based examination combined with multivariate data analyses. Methods are a nondestructive material characterization approach that can provide predictions as to carbon fiber bulk physical properties, as well as identification of unknown carbon fiber materials for quality control purposes. The framework of the multivariate analysis methods includes a principal component-based identification protocol including comparison of Raman spectral data from an unknown carbon fiber with a data library of multiple principal component spaces.

Houk, Amanda L.↗

DOE OSTI2014

Identification of Leakage Spectra from Neutron Activation in Glass/Cherenkov Detectors - Paper 96

Oak Ridge National Laboratory has developed a new detector system concept that can be deployed in major US cities to identify the leakage spectrum of a nuclear weapon detonation. The detector is based on a small piece of glass that has been doped with an element that has a high activation cross section and creates a radioactive activation product with a reasonable length half-life. The decay of the activation product(s) after exposure creates Cherenkov light which can propagate to a photomultiplier and can be turned into a count-rate signal. The signal from each glass in each detector in a city can be individually analyzed to determine the amount of activation products produced in the initial exposure. Several activation products can be determined in a single glass if the half-lives are not the same. With a known source location and a detailed 3D model of a city, neutron transport simulations can be made by using a library of known sources to predict the activation amounts each source would have made in the glass detectors. A simple comparison of the measured activation amounts and the predicted activation amounts can identify the source spectrum contained in the library that is the best match. Choosing dopants with a large range in the threshold energy for the activation reactions can help to differentiate the spectra in the library. The method of matching the measured activation amounts to the predicted activation amounts to identify the source spectrum is similar to the analysis used for the passive Activation Foil Integrated Detector System (AFIDS), also developed at Oak Ridge National Laboratory. In AFIDS, wires or foils of known mass and isotopic composition are deployed before and then collected after exposure. Counting gammas in a nearby laboratory determines the activation amounts. The glass/Cherenkov system is active - it uses a battery-powered detector to count flashes of Cherenkov light and to communicate its count rates to a remote location for further analysis. Work has been performed in several areas, including glass making, automated detection and communication systems and software tools for analysis of the signal and source spectrum identification. Bell and Boatner have developed phosphate glasses that incorporate elements with high capture cross sections, and Hayward has simulated the response with Geant4 and measured the response with isotopic gamma sources. This paper will focus on the software tools for determining the activation amounts from the Cherenkov count-rate signal and finding the best matching source spectrum. A test problem in an urban environment is used to demonstrate the potential of a spectrum identification system using neutron activation. The analysis methods developed to identify the neutron leakage spectra from Cherenkov light given off by neutron activation in doped glasses work well. The calculation used to unfold the count-rate information into the number of actual activation products uses robust algorithms that can also compute associated uncertainties. These uncertainties and the known uncertainties of the glass tube material compositions are incorporated into the matching analysis to determine which of the source spectra in the library best matches the measured activation data. Any measurement method used to identify a neutron source spectrum relies at some point on a comparison against known sources; no identification method is definitive. Detection systems measure some physical aspect of the source, not its serial number. Many systems measure the physical aspect to determine that the source has some property, and then leave it to experts to determine which potential sources share that property. The analysis system presented here incorporates the comparison into the analysis itself. The statistical tests show which of the known library sources match the measured data the best and whether that match is a good match. If the best match still does not fit the measured data well (a very high χ{sup 2} value), that indicates the true source is not one of the sources in the library. This is still valuable information for decision makers. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

A co-registered in-situ and ex-situ dataset from wire arc additive manufacturing process

Recent progress in sensing techniques and data analytics tools have significantly accelerated the development of Wire Arc Additive Manufacturing (WAAM) systems. This data-centric approach emphasizes leveraging sensor data available throughout the production process to optimize performance. Integration of extensive data analysis provides opportunities for improving precision, reducing waste, and enhancing the quality of produced parts. This method relies on AI/ML models and optimization techniques, which are developed using the data collected from various sources, including in-situ sensors, ex-situ imaging, and manufacturing process parameters. The quality and diversity of this data, along with the alignment between different data streams (achieved through spatiotemporal registration) are critical for the successful development of AI/ML and optimization models. In this work, we present a spatiotemporally registered dataset generated during the WAAM process of deposition of a rectangular block. The dataset includes a comprehensive description of the deposition process, process parameters, welding characteristics and acoustic data collected in-situ, and X-Ray Computed Tomography data of the build.

42 ENGINEERING↗

DOE OSTI2014

Fiducial marker-based correction for involuntary motion in weight-bearing C-arm CT scanning of knees. II. Experiment

Purpose: A C-arm CT system has been shown to be capable of scanning a single cadaver leg under loaded conditions by virtue of its highly flexible acquisition trajectories. In Part I of this study, using the 4D XCAT-based numerical simulation, the authors predicted that the involuntary motion in the lower body of subjects in weight-bearing positions would seriously degrade image quality and the authors suggested three motion compensation methods by which the reconstructions could be corrected to provide diagnostic image quality. Here, the authors demonstrate that a flat-panel angiography system is appropriate for scanning both legs of subjectsin vivo under weight-bearing conditions and further evaluate the three motion-correction algorithms using in vivo data. Methods: The geometry of a C-arm CT system for a horizontal scan trajectory was calibrated using the PDS-2 phantom. The authors acquired images of two healthy volunteers while lying supine on a table, standing, and squatting at several knee flexion angles. In order to identify the involuntary motion of the lower body, nine 1-mm-diameter tantalum fiducial markers were attached around the knee. The static mean marker position in 3D, a reference for motion compensation, was estimated by back-projecting detected markers in multiple projections using calibrated projection matrices and identifying the intersection points in 3D of the back-projected rays. Motion was corrected using three different methods (described in detail previously): (1) 2D projection shifting, (2) 2D deformable projection warping, and (3) 3D rigid body warping. For quantitative image quality analysis, SSIM indices for the three methods were compared using the supine data as a ground truth. Results: A 2D Euclidean distance-based metric of subjects’ motion ranged from 0.85 mm (±0.49 mm) to 3.82 mm (±2.91 mm) (corresponding to 2.76 to 12.41 pixels) resulting in severe motion artifacts in 3D reconstructions. Shifting in 2D, 2D warping, and 3D warping improved the SSIM in the central slice by 20.22%, 16.83%, and 25.77% in the data with the largest motion among the five datasets (SCAN5); improvement in off-center slices was 18.94%, 29.14%, and 36.08%, respectively. Conclusions: The authors showed that C-arm CT control can be implemented for nonstandard horizontal trajectories which enabled us to scan and successfully reconstruct both legs of volunteers in weight-bearing positions. As predicted using theoretical models, the proposed motion correction methods improved image quality by reducing motion artifacts in reconstructions; 3D warping performed better than the 2D methods, especially in off-center slices.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2016

The implementation and data analysis of an interferometer for intense short pulse laser experiments

We present an interferometry setup and the detailed fringe analysis method for intense short pulse (SP) laser experiments. The interferometry scheme was refined through multiple campaigns to investigate the effects of pre-plasmas on energetic electrons at the Jupiter Laser Facility at Lawrence Livermore National Laboratory. The interferometer used a frequency doubled ( ${\it\lambda}=0.527~{\rm\mu}\text{m}$ ) 0.5 ps long optical probe beam to measure the pre-plasma density, an invaluable parameter to better understand how varying pre-plasma conditions affect the characteristics of the energetic electrons. The hardware of the diagnostic, data analysis and example data are presented. Here, the diagnostic setup and the analysis procedure can be employed for any other SP laser experiments and interferograms, respectively.

42 ENGINEERING↗

DOE OSTI2020

Performance Analysis of Traditional and Data-Parallel Primitive Implementations of Visualization and Analysis Kernels

Measurements of absolute runtime are useful as a summary of performance when studying parallel visualization and analysis methods on computational platforms of increasing concurrency and complexity. We can obtain even more insights by measuring and examining more detailed measures from hardware performance counters, such as the number of instructions executed by an algorithm implemented in a particular way, the amount of data moved to/from memory, memory hierarchy utilization levels via cache hit/miss ratios, and so forth. This work focuses on performance analysis on modern multi-core platforms of three different visualization and analysis kernels that are implemented in different ways: one is "traditional", using combinations of C++ and VTK, and the other uses a data-parallel approach using VTK-m. Our performance study consists of measurement and reporting of several different hardware performance counters on two different multi-core CPU platforms. The results reveal interesting performance differences between these two different approaches for implementing these kernels, results that would not be apparent using runtime as the only metric.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Analysis of Defects in Metal Additive Manufacturing with Augmented Data Generation

Laser powder bed fusion (LPBF) is a method of additive manufacturing (AM) that selectively melts and fuses together microscopic metallic powder. LPBF offers the benefit of producing custom structures out of high strength metals that can be difficult to fabricate with conventional methods. The challenge of LPBF is that 3D printed structures often have internal pores due to process flaws. Pulsed thermal tomography (PTT) is a method for reconstructing the depth profile of materials, allowing the visualization internal voids in solids. In prior work, we developed a convolutional neural network (CNN) which, having been trained on simulated 2D PTT images of subsurface elliptical defects, was able to classify the semi-major radii, semi-minor radii, and angular orientation of the best-fit ellipses in previously unseen PTT images. The unseen PTT images contained subsurface irregular defect shapes imported from scanning electron microscopy (SEM) images of metallic LPBF-printed specimens. Training the CNN on irregular defect shapes instead of on elliptical shapes would make the resulting classifications more descriptive of actual defect shapes. However, this requires a much higher volume of SEM images of material defects, which are difficult to obtain because of random occurrence of defects in LPBF. To address this challenge, we developed a generative adversarial network (GAN) to augment the existing dataset of SEM defect images. The GAN model is demonstrated to create novel yet realistic defect shapes that can be used as input for simulated PTT images to train CNN.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Delegated Regressor, A Robust Approach for Automated Anomaly Detection in the Soil Radon Time Series Data

We propose a new method based on the idea of delegating regressors for predicting the soil radon gas concentration (SRGC) and anomalies in radon or any other time series data. The proposed method is compared to different traditional boosting e.g., Extreme Gradient Boosting (EGB) and simple regression methods e.g., support vector regressors with linear kernel and radial kernel in terms of accurate predictions. R language has been used for the statistical analysis of radon time series (RTS) data. The results obtained show that the proposed methodology predicts SRGC more accurately when compared to different traditional boosting and regression methods. The best correlation is found between the actual and predicted radon concentration for window size of 2 i.e., two days before and after the start of seismic activities. RTS data was collected from 05 February 2017 to 16 February 2018, including 7 seismic events recorded during the study period. Findings of study show that the proposed methodology predicts the SRGC with more precision, for all the window sizes, by overlapping predicted with the actual radon time series concentrations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Comparing traditional and Bayesian approaches to ecological meta‐analysis

Abstract Despite the wide application of meta‐analysis in ecology, some of the traditional methods used for meta‐analysis may not perform well given the type of data characteristic of ecological meta‐analyses. We reviewed published meta‐analyses on the ecological impacts of global climate change, evaluating the number of replicates used in the primary studies ( n i ) and the number of studies or records ( k ) that were aggregated to calculate a mean effect size. We used the results of the review in a simulation experiment to assess the performance of conventional frequentist and Bayesian meta‐analysis methods for estimating a mean effect size and its uncertainty interval. Our literature review showed that n i and k were highly variable, distributions were right‐skewed and were generally small (median n i = 5, median k = 44). Our simulations show that the choice of method for calculating uncertainty intervals was critical for obtaining appropriate coverage (close to the nominal value of 0.95). When k was low (<40), 95% coverage was achieved by a confidence interval (CI) based on the t distribution that uses an adjusted standard error (the Hartung–Knapp–Sidik–Jonkman, HKSJ), or by a Bayesian credible interval, whereas bootstrap or z distribution CIs had lower coverage. Despite the importance of the method to calculate the uncertainty interval, 39% of the meta‐analyses reviewed did not report the method used, and of the 61% that did, 94% used a potentially problematic method, which may be a consequence of software defaults. In general, for a simple random‐effects meta‐analysis, the performance of the best frequentist and Bayesian methods was similar for the same combinations of factors ( k and mean replication), though the Bayesian approach had higher than nominal (>95%) coverage for the mean effect when k was very low ( k < 15). Our literature review suggests that many meta‐analyses that used z distribution or bootstrapping CIs may have overestimated the statistical significance of their results when the number of studies was low; more appropriate methods need to be adopted in ecological meta‐analyses.

Pappalardo, Paula↗

DOE OSTI2020

Clustering Analysis of Commercial Vehicles Using Automatically Extracted Features from Time Series Data

Standard of practice approaches to time series cluster analysis involve careful feature engineering, often utilizing expert input to tune and select features by hand. In many cases, expert input may not be readily available, or there may not yet exist a community consensus on the ideal features for a given application. This paper compares the results of several cluster analysis methods, using both hand selected features and those extracted automatically, when applied to large geospatial time series telematics data from commercial trucking fleets. The impacts of feature selection, dimensionality reduction, and choice of clustering algorithm on the quality of clustering results are explored. Results from this analysis confirm prior results that domain agnostic features are competitive with the hand engineered features with respect to clustering quality metrics. These results also provide new insight into the most successful strategies for identifying structure in large unstructured vehicle telematics data, and suggest that time series clustering using automatic feature extraction can be an effective approach to extract structure from large scale geospatial time series data in cases when hand selected features are not available.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2013

ESTIMATING THE PROPERTIES OF HARD X-RAY SOLAR FLARES BY CONSTRAINING MODEL PARAMETERS

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23. We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non-Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, E{sub c} , a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that E{sub c} lies below approximately 40 keV, and a 68% probability that it lies in the range 7-36 keV. Further, the low-energy cutoff is more likely to be in the range 25-35 keV than in any other 10 keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 {+-} 4 keV with 68% probability. Using the Bayesian/MCMC approach, we also estimate for the first time probability density functions for the total number of flare-accelerated electrons and the energy they carry for each flare studied. For the 2002 July 23 event, these probability density functions are asymmetric with long tails orders of magnitude higher than the most probable value, caused by the poorly constrained value of the low-energy cutoff. The most probable electron power is estimated at 10{sup 28.1} erg s{sup -1}, with a 68% credible interval estimated at 10{sup 28.1}-10{sup 29.0} erg s{sup -1}, and a 95% credible interval estimated at 10{sup 28.0}-10{sup 30.2} erg s{sup -1}. For the 2005 January 19 flare spectrum, the probability density functions for the total number of flare-accelerated electrons and their energy are much more symmetric and narrow: the most probable electron power is estimated at 10{sup 27.66{+-}0.01} erg s{sup -1} (68% credible intervals). However, in this case the uncertainty due to systematic sources of error is estimated to dominate the uncertainty due to statistical sources of error.

79 ASTRONOMY AND ASTROPHYSICS↗