Results for “Statistical Analysis” — Page 40

NASA NTRS2000

[Compton GRO Cycle 7]

The goals of this project were to use the improved location accuracy of combined BATSE/Ulysses-IPN gamma-ray burst (GRB) data to search for small-angle clustering within the burst population and to search for possible correlations between bursts and catalogs of known astrophysical objects. The research was completed in several phases due to the length of time needed to process the basic BATSE/Ulysses data and to develop the appropriate analysis algorithms. In the first phase, BATSE/Ulysses data were gathered from their respective sources and processed to yield, final BATSE burst catalog locations and final BATSE/Ulysses IPN timing annuli. The final data are published. In the next phase, traditional statistical analysis techniques were used to search a subset of the data for small-angle clustering and. correlations, and to produce upper limits. Next, the unique analysis techniques and software described in the proposal were developed and,applied to the final set of data (corresponding to the 4B catalog). The final search did not find any significant self-clustering or correlations with supernovae, AGN, or near by galaxy clusters. The investigation ruled-out earlier findings that indicated (with marginal significance) such results, and. provided stringent limits on the allowable fraction of bursts that are self-clustered and associated with selected known objects. An added benefit of this research came in 1998 when it was suggested that some gamma-ray bursts may be associated with supernova (SN) explosions. We responded rapidly and applied the tools of this investigation to study this possibility. Using combined BATSE/Ulysses data, we were able to completely rule out any association between bright bursts and known supernovae, thereby questioning the validity of any GRB/SN association. If a GRB/SN association exists, it must be only with a small fraction of weak bursts.

Kippen, R. Marc↗

NASA NTRS2006

Plasmaspheric Drainage Plumes: Inner-Magnetospheric Coupling from the IMAGE/EUV Perspective

Plasmaspheric drainage plumes appear in the aftermath of periods of enhanced convection/erosion and are interpreted as a near-equatorial signature of the redistribution of thermal plasma along streamlines. Analysis of IMAGE/EUV observations from "FirstLight" through the end of calendar year 2002 reveals that for Kp greater than or equal to 3, there is an 84% probability of observing a plasmaspheric plume in EUV data. We present a statistical analysis of the geomagnetic conditions [Kp, Dst, and solar wind-induced electric field] associated with EUV plume observations. This analysis yields a peak in observational probability when Kp = 4 and Dst = -50 nT. Additionally, EUV pllume observations are associated with a solar wind-induced convection electric field at Earth [Ev, SM] characterized by bi-modal behavior with a positive mode peaked at approximately 4 m V(raised dot) m(sup -1) and a negative model that peaks at -2 mV (raised dot) m(sup -1). Analysis of the time rate of change of the plume-associated Ev, SM indicated that once the mechanism for plume formation is initiated, a slowly changing convection environment is required to allow for sufficient plume development prior to EUV detection.

Adrian, Mark L.↗

NASA NTRS1985

Are galactic bulge X-ray burst sources leftovers of distupted globular clusters

Since approximately 1979, it is known that galactic bulge X-ray sources are low-mass binary systems, and that the X-ray bursters are a subset of the bulge sources. Grindlay and Hertz (1983) reported on the close proximity (in four of twelve cases) of an X-ray burst source and a normal star. The two authors believe that these alignments are not coincidental. They suggest that the normal star is surviving giant in a disrupted globular cluster core, of which the X-ray source would also be a member. The present investigation has the objective to show that Grindlay and Hertz made an error in their statistical analysis of a factor of approximately 10. It is, thus, believed that there is insufficient evidence for the conclusion reported by Grindlay and Hertz. On the basis of the present investigation, it is concluded that there exists at present no statistically significant observational evidence that X-ray bursters, presently located outside globular clusters, were formed in globular clusters.

Van Paradijs, J.↗

NASA NTRS1985

Further results of natural laminar flow flight test experiments

Flight test experiments were conducted to measure the extent and nature of natural laminar flow on a smoothed test region of a swept-wing business jet wing. Surface hot film anemometry and sublimating chemicals were used for transition detection. Surface pressure distributions were measured using pressure belts. Engine noise was monitored by a microphone attached to the wing surface to study possible acoustic effects on stability of the laminar boundary layer. Side-slip conditions were flown to simulate changes in effective wing sweep. Flight instrumentation and ground data analysis techniques and a method for measuring intermittency of turbulence are described. Correlation was obtained between the hot film gage signals and chemicals for transition detection. Cross-flow vortices were observed for some flight conditions. Results of spectral and statistical analysis of the hot film signals for various flight test conditions are presented.

Wentz, W. H., Jr.↗

NASA NTRS1985

Magnetic Field-Vector Measurements in Quiescent Prominences via the Hanle Effect: Analysis of Prominences Observed at Pic-Du-Midi and at Sacramento Peak

The Hanle effect method for magnetic field vector diagnostics has now provided results on the magnetic field strength and direction in quiescent prominences, from linear polarization measurements in the He I E sub 3 line, performed at the Pic-du-Midi and at Sacramento Peak. However, there is an inescapable ambiguity in the field vector determination: each polarization measurement provides two field vector solutions symmetrical with respect to the line-of-sight. A statistical analysis capable of solving this ambiguity was applied to the large sample of prominences observed at the Pic-du-Midi (Leroy, et al., 1984); the same method of analysis applied to the prominences observed at Sacramento Peak (Athay, et al., 1983) provides results in agreement on the most probable magnetic structure of prominences; these results are detailed. The statistical results were confirmed on favorable individual cases: for 15 prominences observed at Pic-du-Midi, the two-field vectors are pointing on the same side of the prominence, and the alpha angles are large enough with respect to the measurements and interpretation inaccuracies, so that the field polarity is derived without any ambiguity.

Bommier, V.↗

DOE OSTI2024

Assessment of BQ-9000 Biodiesel Properties for 2023

This is the seventh in a series of reports documenting the quality of biodiesel from U.S.- and Canadian-based producers that participate in the BQ-9000 program, the biodiesel industry’s voluntary quality assurance program. Participants provided monthly data on critical quality parameters for calendar year 2023 with quality data provided to a team of experts, who removed any identifying company information and provided anonymized data to the National Renewable Energy Laboratory (NREL) for statistical analysis. New for 2023, data on kinematic viscosity, sulfated ash, distillation temperature, carbon residue, and cetane were collected, as well as individual levels of sodium, potassium, calcium, and magnesium. Critical quality parameters analyzed are listed in Table ES-1 with descriptive statistics.

09 BIOMASS FUELS↗

NASA NTRS2009

Fused Bead Analysis of Diogenite Meteorites

Bulk rock chemistry is an essential dataset in meteoritics and planetary science [1]. A common method used to obtain the bulk chemistry of meteorites is ICP-MS. While the accuracy, precision and low detection limits of this process are advantageous [2], the sample size used for analysis (approx.70 mg) can be a problem in a field where small and finite samples are the norm. Fused bead analysis is another bulk rock analytical technique that has been used in meteoritics [3]. This technique involves forming a glass bead from ~10 mg of sample and measuring its chemistry using a defocused beam on a microprobe. Though the ICP-MS has lower detection limits than the microprobe, the fused bead method destroys a much smaller sample of the meteorite. Fused bead analysis was initially designed for samples with near-eutectic compositions and low viscosities. Melts generated of this type homogenize at relatively low temperatures and produce primary melts near the sample s bulk composition [3]. The application of fused bead analysis to samples with noneutectic melt compositions has not been validated. The purpose of this study is to test if fused bead analysis can accurately determine the bulk rock chemistry of non-eutectic melt composition meteorites. To determine this, we conduct two examinations of the fused bead. First, we compare ICP-MS and fused bead results of the same samples using statistical analysis. Secondly, we inspect the beads for the presence of crystals and chemical heterogeneity. The presence of either of these would indicate incomplete melting and quenching of the bead.

Mittlefehldt, D.W.↗

NASA NTRSDate not supplied

The System Modeling and Analysis of Resiliency in STEReO (SMARt-STEReO)

Wildfire emergency response has remained rooted in relatively low-tech solutions for coordination between ground and aerial assets. These low-tech solutions are robust for the remote environments in which wildfires are usually fought, but limit strategic cross-organizational support and the ability to deploy and effectively utilize aerial assets. As aircraft become more advanced and new technology, including drones, become available to firefighters, a new, more modern method of asset coordination is needed. NASA is working on a project called ‘Scalable Traffic Management for Emergency Response Operations’ (STEReO) to integrate unmanned aerial systems (UAS)and UAS traffic management (UTM)into wildfire response. STEReO’s goals include simplifying the coordination of aerial assets, improving the existing UAS framework, and increasing the role of additional autonomous systems to reduce human risk and to increase system resilience. This paper describes the development of the ‘System Modeling and Analysis of Resiliency in STEReO’ (SMARt-STEReO) project, which aims to model wildfire response and to quantify the additional system resilience that STEReO technology provides firefighters. This paper verifies SMARt-STEReO and defines its scope; it includes experimental and statistical analysis of the impact that the addition of UAS has on both performance metrics and also on performance resiliency response to a given fault. SMARt-STEReO is a grid-based model of fire propagation that incorporates varying crew responses. Through the use of a Python package called ‘fmdtools’, the model easily allows for the addition of faults to the system. These faults allow analysts to investigate various response parameters. Factors including terrain, fuel type and wind speed can be modified to affect the fire propagation; additionally, the number of ground crews, engines, fixed wing aircraft, helicopters, and UAS can be changed to affect the crew response. The communication lines between actors mimic those used in real life situations. This paper explains the development of SMARt-STEReO including background research, verification and validation, and preliminary experimental analysis of system resilience to both a minor and major fault in systems with and without UAS.

Resiliency↗

NASA NTRS2022

Estimating pixel-level uncertainty in ocean color retrievals from MODIS

The spectral distribution of marine remote sensing reflectance, R(rs), is the fundamental measurement of ocean color science, from which a host of bio-optical and biogeochemical properties of the water column can be derived. Estimation of uncertainty in these derived properties is thus dependent on knowledge of the uncertainty in satellite-retrieved R(rs) (u(c)(R(rs))) at each pixel. Uncertainty in R(rs), in turn, is dependent on the propagation of various uncertainty sources through the R(rs) retrieval process, namely the atmospheric correction (AC). A derivative-based method for uncertainty propagation is established here to calculate the pixel-level uncertainty in R(rs), as retrieved using NASA’s multiple-scattering epsilon (MSEPS) AC algorithm and verified using Monte Carlo (MC) analysis. The approach is then applied to measurements from the Moderate Resolution Imaging Spectroradiometer (MODIS) on the Aqua satellite, with uncertainty sources including instrument random noise, instrument systematic uncertainty, and forward model uncertainty. The uc(Rrs) is verified by comparison with statistical analysis of coincident retrievals from MODIS and in situ Rrs measurements, and our approach performs well in most cases. Based on analysis of an example 8-day global products, we also show that relative uncertainty in R(rs) at blue bands has a similar spatial pattern to the derived concentration of the phytoplankton pigment chlorophyll-a (chl-a), and around 7.3%, 17.0%, and 35.2% of all clear water pixels (chl-a ≤ 0.1 mg/cu.m) with valid u(c)(R(rs)) have a relative uncertainty ≤ 5% at bands 412 nm, 443 nm, and 488 nm respectively, which is a common goal of ocean color retrievals for clear waters. While the analysis shows that u(c)(R(rs)) calculated from our derivative-based method is reasonable, some issues need further investigation, including improved knowledge of forward model uncertainty and systematic uncertainty in instrument calibration.

Pixel-level uncertainty↗

NASA NTRS2019

Using Gaia Data 2 to Constrain Local Dark Matter Density and Thin Dark Disk

We use stellar kinematics from the latest Gaia data release (DR2) to measure the local dark matter (DM) density ρDM in a heliocentric cylinder of radius R = 150 pc and half-height z = 200 pc. We also explore the prospect of using our analysis to estimate the DM density in local substructure by setting constraints on the surface density and scale height of a thin dark disk aligned with the baryonic disk and formed due to dissipative dark matter self-interactions. Performing the statistical analysis within a Bayesian framework for three types of tracers, we obtain ρDM = 0.016 ± 0.010 Mꙩ/p c 3 for A stars; early G stars give a similar result, while F stars yield a significantly higher value. For a thin dark disk, A stars set the strongest constraint: excluding surface densities (5–12) Mꙩ/pc 2 for scale heights below 100 pc with 95% confidence. The upper bound of this constraint implies . 1% of the Milky Way DM mass is present in a dissipative dark sector. Comparing our results with those derived using Tycho-Gaia Astrometric Solution (TGAS) data, we find that the uncertainty in our measurements of the local DM content is dominated by systematic errors that arise from assumptions of our dynamical analysis in the low z region. Furthermore, there will only be a marginal reduction in these uncertainties with more data in the Gaia era. We comment on the robustness of our method and discuss potential improvements for future work.

dark matter theory↗

DOE OSTI2025

Concentration-Discharge Relationships in the Six Largest Arctic Rivers, 2003-2019

This dataset provides the results of the analysis of the relationship of dissolved analyte concentrations and river discharges in the six largest Arctic rivers across the global panarctic region (see Figure 1 in documentation file *.pdf). Long-term measurements of dissolved analyte concentrations and river discharge have been collected for each of the Kolyma, Lena, Mackenzie, Ob, Yenisey, and Yukon rivers by the Arctic Great Rivers Observatory (ArcticGRO) project from ~2003-present (Shiklomanov, 2021). The relationship of dissolved analyte concentrations and discharges in each river was characterized by statistical analysis of the slope of the log(concentration) vs log(discharge) (b), the coefficient of variation ratio (CVc/CVq), the 2.5% and 97.5% confidence intervals of b, and assigning a chemostatic, flushing, diluting, or non-systematic behavior category according to Koger (2018). The summary of these analyses for all six rivers is provided in one .csv file. The concentrations of 20 dissolved analytes and discharge measurement data for the individual Kolyma, Lena, Mackenzie, Ob, Yenisey, and Yukon rivers are also provided with this dataset. There are seven *.csv files; one for each river plus the statistical summary. These public ArcticGRO data at "https://www.arcticgreatrivers.org" (Shiklomanov, 2021) were downloaded on Feb 13, 2020, but each river has different measurement dates over the sampling and analysis period. The ArcticGRO metadata document (*.pdf) downloaded on Feb 13, 2020 is also included in this dataset. The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research. The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Comparative Analyses of Bioequivalence Assessment Methods for In Vitro Permeation Test Data

ABSTRACT For topical, dermatological drug products, an in vitro option to determine bioequivalence (BE) between test and reference products is recommended. In particular, in vitro permeation test (IVPT) data analysis uses a reference‐scaled approach for two primary endpoints, cumulative penetration amount (AMT) and maximum flux ( J max ), which takes the within donor variability into consideration. In 2022, the Food and Drug Administration (FDA) published a draft IVPT guidance that includes statistical analysis methods for both balanced and unbalanced cases of IVPT study data. This work presents a comprehensive evaluation of various methodologies used to estimate critical parameters essential in assessing BE. Specifically, we investigate the performance of the FDA draft IVPT guidance approach alongside alternative empirical and model‐based methods utilizing mixed‐effects models. Our analyses include both simulated scenarios and real‐world studies. In simulated scenarios, empirical formulas consistently demonstrate robustness in approximating the true model, particularly in effectively addressing treatment–donor interactions. Conversely, the effectiveness of model‐based approaches heavily relies on precise model selection, which significantly influences their results. The research emphasizes the importance of accurate model selection in model‐based BE assessment methodologies. It sheds light on the advantages of empirical formulas, highlighting their reliability compared to model‐based approaches and offers valuable implications for BE assessments. Our findings underscore the significance of robust methodologies and provide essential insights to advance their understanding and application in the assessment of BE, employed in IVPT data analysis.

Leon, Sami↗

DOE OSTI2020

Soil microbial function and fungal community data along an ectomycorrhizal basal area gradient, Vermont, May 2019

Mycorrhizal fungi can affect soil organic matter cycling through several mechanisms including priming, nutrient competition, and direct enzyme production. Differences in nutrient foraging strategies between ectomycorrhizal (EcM) and arbuscular mycorrhizal (AM) fungi produce divergent belowground dynamics: where EcM can take up organic nitrogen and directly break down SOM by producing enzymes, AM fungi are limited to scavenging mineral N. EcM-associated tree species also have leaf litter with relatively higher ratios of carbon to nitrogen (C:N), and belowground saprotrophic communities more dominated by fungi. Consequently, free-living microbes in EcM-dominated soils should experience nitrogen limitation, with subsequent increases in enzyme production and decreased carbon use efficiency (CUE). However, the relative importance of the effects of substrate quality and fungal community composition on enzyme production and CUE are unclear. To assess this distinction, we sampled the organic horizon and 10 cm of the mineral horizon in northern temperate forest soils along a gradient of EcM dominance (see SCxTS_DBH.csv for full tree species information). We characterized fungal community composition by measuring EcM relative abundances from extracted fungal DNA (To run raw ASV data through R code, use SCxTS_ASV_taxonomy.csv, and R code ITS_processing.Rmd; to see processed data with EcM relative abundance, use file SCxTS_sum_afitch_Feb18.20.csv) and the fungal to bacterial ratios (see data file SCxTS_plfa.csv) from phospholipid fatty acid analysis. Soil microbial functions were measured as potential activities of five hydrolytic and two oxidative enzymes ( To run raw data through R code us SCxTS_metadata.csv, hydrolytic_oxidative_raw.csv, MUBraw.csv, Enzyme_soilweight.csv, and incubationtime.csv, and R code SCxTS_enzymes.Rmd; to use Enzyme data ready to run through statistics code, use file Enzyme.data.csv) and microbial carbon use efficiency (see file SCxTS_CUE.csv and for full calculations file 18O_CUEcalcs_SCxTS_2019.xlsx). We assessed soil substrate quality as the soil carbon:nitrogen ratio (See file Organic_CN.csv). Statistical analysis can be run using R code from file SCxTS_analysis.Rmd.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis: Version 6.12 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis (V.6.14) (Theory Manual)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.13 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Theory Manual (V.6.15)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.16 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota’s iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗