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At least 19 records

A Poisson process approximation for generalized K-5 confidence regions

One-sided confidence regions for continuous cumulative distribution functions are constructed using empirical cumulative distribution functions and the generalized Kolmogorov-Smirnov distance. The band width of such regions becomes narrower in the right or left tail of the distribution. To avoid tedious computation of confidence levels and critical values, an approximation based on the Poisson process is introduced. This aproximation provides a conservative confidence region; moreover, the approximation error decreases monotonically to 0 as sample size increases. Critical values necessary for implementation are given. Applications are made to the areas of risk analysis, investment modeling, reliability assessment, and analysis of fault tolerant systems.

Arsham, H.

Confidence regions of planar cardiac vectors

A method for plotting the confidence regions of vectorial data obtained in electrocardiology is presented. The 90%, 95% and 99% confidence regions of cardiac vectors represented in a plane are obtained in the form of an ellipse centered at coordinates corresponding to the means of a sample selected at random from a bivariate normal distribution. An example of such a plot for the frontal plane QRS mean electrical axis for 80 horses is also presented.

Dubin, S.

Program for Weibull Analysis of Fatigue Data

A Fortran computer program has been written for performing statistical analyses of fatigue-test data that are assumed to be adequately represented by a two-parameter Weibull distribution. This program calculates the following: (1) Maximum-likelihood estimates of the Weibull distribution; (2) Data for contour plots of relative likelihood for two parameters; (3) Data for contour plots of joint confidence regions; (4) Data for the profile likelihood of the Weibull-distribution parameters; (5) Data for the profile likelihood of any percentile of the distribution; and (6) Likelihood-based confidence intervals for parameters and/or percentiles of the distribution. The program can account for tests that are suspended without failure (the statistical term for such suspension of tests is "censoring"). The analytical approach followed in this program for the software is valid for type-I censoring, which is the removal of unfailed units at pre-specified times. Confidence regions and intervals are calculated by use of the likelihood-ratio method.

Krantz, Timothy L.

The Error Distribution of BATSE GRB Location

We develop empirical probability models for BATSE GRB location errors by a Bayesian analysis of the separations between BATSE GRB locations and locations obtained with the InterPlanetary Network (IPN). Models are compared and their parameters estimated using 394 GRBs with single IPN annuli and 20 GRBs with intersecting IPN annuli. Most of the analysis is for the 4B (rev) BATSE catalog; earlier catalogs are also analyzed. The simplest model that provides a good representation of the error distribution has 78% of the locations in a 'core' term with a systematic error of 1.85 degrees and the remainder in an extended tail with a systematic error of 5.36 degrees, implying a 68% confidence region for bursts with negligible statistical errors of 2.3 degrees. There is some evidence for a more complicated model in which the error distribution depends on the BATSE datatype that was used to obtain the location. Bright bursts are typically located using the CONT datatype, and according to the more complicated model, the 68% confidence region for CONT-located bursts with negligible statistical errors is 2.0 degrees.

Briggs, Michael S.

Parameter estimation in X-ray astronomy using maximum likelihood

Methods of estimation of parameter values and confidence regions by maximum likelihood and Fisher efficient scores starting from Poisson probabilities are developed for the nonlinear spectral functions commonly encountered in X-ray astronomy. It is argued that these methods offer significant advantages over the commonly used alternatives called minimum chi-squared because they rely on less pervasive statistical approximations and so may be expected to remain valid for data of poorer quality. Extensive numerical simulations of the maximum likelihood method are reported which verify that the best-fit parameter value and confidence region calculations are correct over a wide range of input spectra.

Wachter, K.

Asymmetric errors

We present a procedure for handling asymmetric errors. Many results in particle physics are presented as values with different positive and negative errors, and there is no consistent procedure for handling them. We consider the difference between errors quoted, using pdfs and using likelihoods, and the difference between the rms spread of a measurement and the 68% central confidence region. We provide a comprehensive analysis of the possibilities, and software tools to enable their use.

Asymmetric

Decadal Seasonal Shifts of Precipitation and Temperature in TRMM and AIRS Data

We present results from an analysis of seasonal phase shifts in the global precipitation and surface temperatures. We use data from the TRMM (Tropical Rainfall Measuring Mission) Multi-satellite Precipitation Algorithm (TMPA), and the Atmospheric Infrared Sounder (AIRS) on Aqua satellite, all hosted at NASA Goddard Earth Science Data and Information Services Center (GES DISC). We explore the information content and data usability by first aggregating daily grids from the entire records of both missions to pentad (5-day) series which are then processed using Singular Value Decomposition approach. A strength of this approach is the normalized principal components that can then be easily converted from real to complex time series. Thus, we can separate the most informative, the seasonal, components and analyze unambiguously for potential seasonal phase drifts. TMPA and AIRS records represent correspondingly 20 and 15 years of data, which allows us to run simple “phase learning†from the first 5 years of records and use it as reference. The most recent 5 years are then phase-compared with the reference. We demonstrate that the seasonal phase of global precipitation and surface temperatures has been stable in the past two decades. However, a small global trend of delayed precipitation, and earlier arrival of surface temperatures seasons, are detectable at 95% confidence level. Larger phase shifts are detectable at regional level, in regions recognizable from the Eigen vectors to having strong seasonal patterns. For instance, in Central North America, including the North American Monsoon region, confident phase shifts of 1-2 days per decade are detected at 95% confidence level. While seemingly symbolic, these shifts are indicative of larger changes in the Earth Climate System. We thus also demonstrate a potential usability scenario of Earth Science Data Records curated at the NASA GES DISC in partnership with Earth Science Missions.

surface temperatures

Fermi Large Area Telescope Second Source Catalog

We present the second catalog of high-energy gamma-ray sources detected by the Large Area Telescope (LAT), the primary science instrument on the Fermi Gamma-ray Space Telescope (Fermi), derived from data taken during the first 24 months of the science phase of the mission, which began on 2008 August 4. Source detection is based on the average flux over the 24-month period. The Second Fermi-LAT catalog (2FGL) includes source location regions, defined in terms of elliptical fits to the 95% confidence regions and spectral fits in terms of power-law, exponentially cutoff power-law, or log-normal forms. Also included are flux measurements in 5 energy bands and light curves on monthly intervals for each source. Twelve sources in the catalog are modeled as spatially extended. We provide a detailed comparison of the results from this catalog with those from the first Fermi-LAT catalog (1FGL). Although the diffuse Galactic and isotropic models used in the 2FGL analysis are improved compared to the 1FGL catalog, we attach caution flags to 162 of the sources to indicate possible confusion with residual imperfections in the diffuse model. The 2FGL catalog contains 1873 sources detected and characterized in the 100 11eV to 100 GeV range of which we consider 127 as being firmly identified and 1171 as being reliably associated with counterparts of known or likely gamma-ray-producing source classes.

Nolan, P. L.

Monte Carlo simulation of errors in the anisotropy of magnetic susceptibility - A second-rank symmetric tensor

Monte Carlo perturbations of synthetic tensors to evaluate the Hext/Jelinek elliptical confidence regions for anisotropy of magnetic susceptibility (AMS) eigenvectors are used. When the perturbations are 33 percent of the minimum anisotropy, both the shapes and probability densities of the resulting eigenvector distributions agree with the elliptical distributions predicted by the Hext/Jelinek equations. When the perturbation size is increased to 100 percent of the minimum eigenvalue difference, the major axis of the 95 percent confidence ellipse underestimates the observed eigenvector dispersion by about 10 deg. The observed distributions of the principal susceptibilities (eigenvalues) are close to being normal, with standard errors that agree well with the calculated Hext/Jelinek errors. The Hext/Jelinek ellipses are also able to describe the AMS dispersions due to instrumental noise and provide reasonable limits for the AMS dispersions observed in two Hawaiian basaltic dikes. It is concluded that the Hext/Jelinek method provides a satisfactory description of the errors in AMS data and should be a standard part of any AMS data analysis.

Lienert, Barry R.

Relationship of Interplanetary Shock Micro and Macro Characteristics: A Wind Study

The non-linear least squared MHD fitting technique of Szabo 11 9941 has been recently further refined to provide realistic confidence regions for interplanetary shock normal directions and speeds. Analyzing Wind observed interplanetary shocks from 1995 to 200 1, macro characteristics such as shock strength, Theta Bn and Mach numbers can be compared to the details of shock micro or kinetic structures. The now commonly available very high time resolution (1 1 or 22 vectors/sec) Wind magnetic field data allows the precise characterization of shock kinetic structures, such as the size of the foot, ramp, overshoot and the duration of damped oscillations on either side of the shock. Detailed comparison of the shock micro and macro characteristics will be given. This enables the elucidation of shock kinetic features, relevant for particle energization processes, for observations where high time resolution data is not available. Moreover, establishing a quantitative relationship between the shock micro and macro structures will improve the confidence level of shock fitting techniques during disturbed solar wind conditions.

Szabo, Adam

Informed total-error-minimizing priors: Interpretable cosmological parameter constraints despite complex nuisance effects

While Bayesian inference techniques are standard in cosmological analyses, it is common to interpret resulting parameter constraints with a frequentist intuition. This intuition can fail, for example, when marginalizing high-dimensional parameter spaces onto subsets of parameters, because of what has come to be known as projection effects or prior volume effects. We present the method of informed total-error-minimizing (ITEM) priors to address this problem. An ITEM prior is a prior distribution on a set of nuisance parameters, such as those describing astrophysical or calibration systematics, intended to enforce the validity of a frequentist interpretation of the posterior constraints derived for a set of target parameters (e.g., cosmological parameters). Our method works as follows. For a set of plausible nuisance realizations, we generate target parameter posteriors using several different candidate priors for the nuisance parameters. We reject candidate priors that do not accomplish the minimum requirements of bias (of point estimates) and coverage (of confidence regions among a set of noisy realizations of the data) for the target parameters on one or more of the plausible nuisance realizations. Of the priors that survive this cut, we select the ITEM prior as the one that minimizes the total error of the marginalized posteriors of the target parameters. As a proof of concept, we applied our method to the density split statistics measured in Dark Energy Survey Year 1 data. We demonstrate that the ITEM priors substantially reduce prior volume effects that otherwise arise and that they allow for sharpened yet robust constraints on the parameters of interest.

79 ASTRONOMY AND ASTROPHYSICS

Analysis of complete quasar samples to obtain parameters of luminosity and evolution functions

A parametric likelihood analysis of the joint redshift-luminosity distribution is presented for a composite, complete sample of 32 quasars with B between 17.0 and 19.2 selected on the basis of ultraviolet excess. Best estimates and joint confidence regions are determined for the parameters of several models of the quasar optical luminosity and evolution function. These models are also tested explicitly for their acceptability. A steeper luminosity function is found than was found for previous samples. A model invoking pure density evolution is rejected on the basis of its extrapolation to fainter magnitudes through comparisons with the optical number counts and independently with the observed 2 keV X-ray background. Assuming an average value for L(x)/L(opt), the contribution of quasars to the X-ray background at 2 keV is discussed.

Marshall, H. L.

Fast and optimal solution to the Rankine-Hugoniot problem

A new, definitive, reliable and fast iterative method is described for determining the geometrical properties of a shock (i.e., theta sub Bn, yields N, V sub s and M sub A), the conservation constants and the self-consistent asymptotic magnetofluid variables, that uses the three dimensional magnetic field and plasma observations. The method is well conditioned and reliable at all theta sub Bn angles regardless of the shock strength or geometry. Explicit proof of uniqueness of the shock geometry solution by either analytical or graphical methods is given. The method is applied to synthetic and real shocks, including a bow shock event and the results are then compared with those determined by preaveraging methods and other iterative schemes. A complete analysis of the confidence region and error bounds of the solution is also presented.

Vinas, A. F.

Fast and optimal solution to the 'Rankine-Hugoniot problem'

A new, definitive, reliable and fast iterative method is described for determining the geometrical properties of a shock (i.e., theta sub Bn, yields N, V sub s and M sub A), the conservation constants and the self-consistent asymptotic magnetofluid variables, that uses the three dimensional magnetic field and plasma observations. The method is well conditioned and reliable at all theta sub Bn angles regardless of the shock strength or geometry. Explicit proof of uniqueness of the shock geometry solution by either analytical or graphical methods is given. The method is applied to synthetic and real shocks, including a bow shock event and the results are then compared with those determined by preaveraging methods and other iterative schemes. A complete analysis of the confidence region and error bounds of the solution is also presented.

Vinas, A. F.

Associated with aerospace vehicles development of methodologies for the estimation of thermal properties

Thermal stress analyses are an important aspect in the development of aerospace vehicles at NASA-LaRC. These analyses require knowledge of the temperature distributions within the vehicle structures which consequently necessitates the need for accurate thermal property data. The overall goal of this ongoing research effort is to develop methodologies for the estimation of the thermal property data needed to describe the temperature responses of these complex structures. The research strategy undertaken utilizes a building block approach. The idea here is to first focus on the development of property estimation methodologies for relatively simple conditions, such as isotropic materials at constant temperatures, and then systematically modify the technique for the analysis of more and more complex systems, such as anisotropic multi-component systems. The estimation methodology utilized is a statistically based method which incorporates experimental data and a mathematical model of the system. Several aspects of this overall research effort were investigated during the time of the ASEE summer program. One important aspect involved the calibration of the estimation procedure for the estimation of the thermal properties through the thickness of a standard material. Transient experiments were conducted using a Pyrex standard at various temperatures, and then the thermal properties (thermal conductivity and volumetric heat capacity) were estimated at each temperature. Confidence regions for the estimated values were also determined. These results were then compared to documented values. Another set of experimental tests were conducted on carbon composite samples at different temperatures. Again, the thermal properties were estimated for each temperature, and the results were compared with values obtained using another technique. In both sets of experiments, a 10-15 percent off-set between the estimated values and the previously determined values was found. Another effort was related to the development of the experimental techniques. Initial experiments required a resistance heater placed between two samples. The design was modified such that the heater was placed on the surface of only one sample, as would be necessary in the analysis of built up structures. Experiments using the modified technique were conducted on the composite sample used previously at different temperatures. The results were within 5 percent of those found using two samples. Finally, an initial heat transfer analysis, including conduction, convection and radiation components, was completed on a titanium sandwich structural sample. Experiments utilizing this sample are currently being designed and will be used to first estimate the material's effective thermal conductivity and later to determine the properties associated with each individual heat transfer component.

Scott, Elaine P.

A Sequence of Outbursts from the Transient X-Ray Pulsar GS 0834-430

GS 0834-430, a 12.3 s accretion-powered pulsar, has been observed in seven outbursts with the BATSE large-area detectors on the Compton Gamma Ray Observatory. The first five outbursts observed by BATSE occurred at intervals of about 107 days, while the final two outbursts were separated by about 140 days. The photon energy spectrum, measured by Earth occultation in the 20 100 keV band, can be fitted by a power law with photon index alpha approximately equals -3.7 or by an exponential spectrum with temperature kT approximately equals 15 keV, with some variations within outbursts. The source has a low pulse fraction, less than or equal to 0.15 in the 20-50 keV band. We have observed significant temporal and energy-dependent variations in epoch folded pulse profiles. Because the intrinsic torque effects for this system are at least comparable to orbital effects, pulse timing analysis did not produce a unique orbital solution. However, confidence regions for the orbital elements yielded the following 1 sigma limits: orbital period P(sub orb) = 105.8 +/- 0.4 days and eccentricity 0.10 less than or approximately equals epsilon less than or approximately equals 0.17. GS 0834-430 is most likely a Be/X-ray binary.

Wilson, Colleen A.

Chandra X-Ray Observations of the Two Brightest Unidentified High Galactic Latitude Fermi-LAT Gamma-Ray Sources

We present Chandra ACIS-I X-ray observations of 0FGL J1311.9−3419 and 0FGL J1653.4−0200, the two brightest high Galactic latitude (absolute value (beta) >10 deg) gamma-ray sources from the three-month Fermi Large Area Telescope (LAT) bright source list that are still unidentified. Both were also detected previously by EGRET, and despite dedicated multi-wavelength follow-up, they are still not associated with established classes of gamma-ray emitters like pulsars or radio-loud active galactic nuclei. X-ray sources found in the ACIS-I fields of view are cataloged, and their basic properties are determined. These are discussed as candidate counterparts to 0FGL J1311.9−3419 and 0FGL J1653.4−0200, with particular emphasis on the brightest of the 9 and 13 Chandra sources detected within the respective Fermi-LAT 95% confidence regions. Further follow-up studies, including optical photometric and spectroscopic observations, are necessary to identify these X-ray candidate counterparts in order to ultimately reveal the nature of these enigmatic gamma-ray objects.

galactic