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Beyond δ : Tailoring marked statistics to reveal modified gravity
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On the relative velocity distribution for general statistics and an application to big-bang nucleosynthesis under Tsallis statistics
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Statistical state dynamics-based study of the stability of the mean statistical state of wall-bounded turbulence
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On the estimation of statistical uncertainties on powder diffraction and small-angle scattering data from two-dimensional X-ray detectors
Optimal methods are explored for obtaining one-dimensional powder pattern intensities from two-dimensional planar detectors with good estimates of their standard deviations. Methods are described to estimate uncertainties when the same image is measured in multiple frames as well as from a single frame. The importance of considering the correlation of diffraction points during the integration and the resampling process of data analysis is shown. It is found that correlations between adjacent pixels in the image can lead to seriously overestimated uncertainties if such correlations are neglected in the integration process. Off-diagonal entries in the variance–covariance (VC) matrix are problematic as virtually all data processing and modeling programs cannot handle the full VC matrix. It is shown that the off-diagonal terms come mainly from the pixel-splitting algorithm used as the default integration algorithm in many popular two-dimensional integration programs, as well as from rebinning and resampling steps later in the processing. When the full VC matrix can be propagated during the data reduction, it is possible to get accurate refined parameters and their uncertainties at the cost of increasing computational complexity. However, as this is not normally possible, the best approximate methods for data processing in order to estimate uncertainties on refined parameters with the greatest accuracy from just the diagonal variance terms in the VC matrix is explored.
Assessing the Ability of Generative Adversarial Networks to Learn Canonical Medical Image Statistics
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Multifidelity Statistical Analysis of Large Eddy Simulations in Scramjet Computations.
Abstract not provided.
Millimeter-wave Point Sources from the 2500 Square Degree SPT-SZ Survey: Catalog and Population Statistics
In this work, we present a catalog of emissive point sources detected in the SPT-SZ survey, a contiguous 2530- square-degree area surveyed with the South Pole Telescope (SPT) from 2008 - 2011 in three bands centered at 95, 150, and 220GHz. The catalog contains 4845 sources measured at a significance of 4.5σ or greater in at least one band, corresponding to detections above approximately 9.8, 5.8, and 20.4 mJy in 95, 150, and 220 GHz, respectively. Spectral behavior in the SPT bands is used for source classification into two populations based on the underlying physical mechanisms of compact, emissive sources that are bright at millimeter wavelengths: synchrotron radiation from active galactic nuclei and thermal emission from dust. The latter population includes a component of high-redshift sources often referred to as submillimeter galaxies (SMGs). In the relatively bright flux ranges probed by the survey, these sources are expected to be magnified by strong gravitational lensing. The survey also contains sources consistent with protoclusters, groups of dusty galaxies at high redshift undergoing collapse. We cross-match the SPT-SZ catalog with external catalogs at radio, infrared, and X-ray wavelengths and identify available redshift information. The catalog splits into 3980 synchrotron-dominated and 865 dust-dominated sources and we determine a list of 506 SMGs. Ten sources in the catalog are identified as stars. We calculate number counts for the full catalog, and synchrotron and dusty components, using a bootstrap method and compare our measured counts with models. This paper represents the third and final catalog of point sources in the SPT-SZ survey.
Comparison between reflectivity statistics at heights of 3 and 6 km and rain rate statistics at ground level
An experiment was conducted to study the relations between the empirical distribution functions of reflectivity at specified locations above the surface and the corresponding functions at the surface. A bistatic radar system was used to measure continuously the scattering cross section per unit volume at heights of 3 and 6 km. A frequency of 3.7 GHz was used in the tests. It was found that the distribution functions for reflectivity may significantly change with height at heights below the level of the melting layer.
Signal statistics of the radar echoes: Angle-of-arrival statistics, part 2.2A
The Doppler spectra, measured with a vertical antenna beam, are characterized by essentially two different kinds of distributions, one has a very narrow and the other a broad spectral width. The former is accepted as due to reflection whereas the latter is due to scattering. It can happen that both kinds of spectra are observed simultaneously. Superimposed on a fairly broad Gaussian signal spectrum, very narrow signal spikes are evident. Because some spikes occur at different Doppler frequencies, the subreflections have to be assumed to move with different radial velocities. To experimentally verify this reasonable assumption, it is proposed to measure the angle of arrival of the different signal returns. One can here make use of the essential advantage that the spikes can be filtered in frequency (called Doppler sortening or sharpening). By means of the cross spectrum analysis with the interferometer technique (measuring phase differences between spaced antennas), their angle of arrival can be measured. This will allow determination of the distribution of the angles of arrival.
Statistical Inference given Summary Statistics in Chemical Models.
Abstract not provided.
QP Statistics Spotlight: Practical versus Statistical Priorities
Randomization during data collection in a designed experiment is an effective strategy for reducing system bias and ensuring independent observations1, but at what cost should it be fully implemented? We recently encountered a scenario that highlights an important aspect of collaboration2 between statisticians, scientists and engineers – the idea of compromise for the sake of achieving wins for all team members. In a multi-million-dollar experiment with a fixed amount of time on the test equipment, each experimental run involved resetting the input values and then waiting for the continuous process to reach a new equilibrium. For example, the temperature of the furnace could be reset, but it takes some time for the test chamber to reach the new temperature and rest at that temperature for a while until all components in the chamber settle at that new setting. Similarly, a critical gas flow component also required a settling period before data could be collected that would be representative of that input setting value. In all, the experiment involved 5 factors, where 4 of the 5 were time-consuming and costly to adjust, with the duration of time needed to reach new equilibrium being dependent on how far the previous setting was from the new one for the combination of these 4 factors. For example, changing from 150° to 200° would reach equilibrium faster than changing from 100° to 200°.
(U) A General-Purpose Code for Correlated Sampling Using Batch Statistics with MCNP6 for Fixed-Source Problems
Correlated sampling can be used to reduce the uncertainty of a difference of tallies by taking advantage of the negative covariance term in the sandwich formula. Booth first showed how correlated sampling can be applied with batch statistics using MCNP’s tally fluctuation chart (TFC) to reduce the uncertainty of a difference of tallies in fixed-source problems. Booth presented a problem in which a 1273% uncertainty in a difference was reduced to 8% by accounting for correlations. Researchers He and Su recently studied correlated sampling using the TFC in MCNP version 5. They determined that the code did not print enough digits in the TFC tally means for accurate batch statistics in some cases. After modifying the source code, they concluded that “correlated sampling can yield a standard deviation of about one magnitude smaller than that predicted by the direct, un-correlated simulation when the changes in system response are small (say about 1%), which is equivalent to saving in CPU time by a factor of 100. Such saving [sic] becomes less significant as the change in system response becomes larger.” He and Su provided the formulas needed to apply batch statistics to compute the correlated uncertainty of a difference of tallies. In this report, we follow up on their work by providing the formulas needed to apply batch statistics to compute the correlated uncertainty of a ratio of tallies and of a difference of two tallies divided by a third tally. We extend these formulas to differences and ratios of ratios. These formulas are applied to reduce the uncertainty associated with calculating a relative sensitivity. He and Su did not investigate the accuracy of their correlated sampling uncertainty estimates. We use their test problems and evaluate the accuracy of the uncertainty estimates by comparing with results obtained from random sampling, and, in simple cases, with theoretical values of the “exact” uncertainties. We find that the uncertainties obtained from batch statistics are accurate as long as at least 100 batches are used. We present a new computer code, COSUBS (COrrelated Sampling Using Batch Statistics), that reads MCNP6 TFCs and applies correlated sampling using batch statistics for the tally combinations that the user specifies. COSUBS is a very general tool that compares all TFCs for a base case and one or two perturbed cases. It computes uncertainties for ratios if given only a base case. This report is organized as follows. The equations to apply batch statistics to the difference of random tallies are reviewed in Sec. II. Section III presents the equations for applying batch statistics to a ratio of random tallies; this is useful for computing relative sensitivities using a one-sided finite difference and the relative sensitivity using the differential operator method. Section IV presents the equations for applying batch statistics to a difference of two random tallies divided by a third; this is useful for computing a relative sensitivities using a central difference. Section V presents the equations for applying batch statistics to a difference of two ratios with four random tallies. Section VI presents the equations for applying batch statistics to a one-sided finite difference estimate of the relative sensitivity of a ratio (this uses four random tallies). Section VII presents the equations for applying batch statistics to a central difference estimate of the relative sensitivity of a ratio (this uses six random tallies). Section VIII presents the equations for applying batch statistics to a sum of random tallies. Section IX discusses how to apply batch statistics using MCNP6. Section X presents COSUBS, describing its command-line options and logic. Sections XI through XVI present numerical results for various test problems. Section XVII is a summary and conclusions. Appendix A derives the theoretical Monte Carlo tally variance given certain assumptions; these variances are used to verify the batch statistics for some of the problems. Appendix B lists the MCNP6 input for the unperturbed example problem. Appendix C presents modifications made to MCNP6.3 to support this work.
Prediction on Underestimation of Statistical Uncertainty in Monte Carlo Eigenvalue Calculation for Two-dimensional Heterogeneous Color Set Geometry
In a Monte Carlo calculation, statistical uncertainty is inevitably included in the result. The statistical uncertainty is commonly estimated by the central limit theorem without considering correlation among generations. The statistical uncertainty is usually expected to decrease at the inverse square root of the number of neutron histories. However, in a Monte Carlo eigenvalue calculation in a large geometry whose dominance ratio is close to unity, the central limit theorem would not be valid and thus the statistical uncertainty of fission source distribution can be significantly underestimated when inter-cycle correlation is not appropriately taken into account. The true statistical uncertainty can be calculated by statistical processing of the results obtained by multiple Monte Carlo runs using different initial random seeds, but this approach has a drawback of large calculation cost. Therefore, prediction of true statistical uncertainty by alternate approach is desirable. One of the solutions for this issue is an evaluation method of statistical uncertainty based on the eigenfunction expansion and the Autoregressive model (AR model). In this method, the true statistical uncertainty is theoretically derived by applying the AR model to behavior of expansion coefficients of eigenfunction in fission source distribution during cycles. Underestimation ratio of statistical uncertainty of fission source distribution can be predicted by this method. Note that the underestimation ratio of statistical uncertainty is defined by the ratio of estimated error by a Monte Carlo calculation to the true statistical error. In the previous study, the proposed method was verified in a simple condition such as one energy group, one dimensional homogeneous slab geometry. Contributions of this summary are as follows. Firstly, expression of the noise term that is appeared in the AR model is theoretically derived. Secondly, prediction on underestimation ratio of statistical uncertainty is carried out in a more general case, i.e., flux of each fuel cell in 2 x 2 heterogeneous assembly geometry taken from the C5G7 benchmark problem. Through the present study, applicability of the theoretical prediction for underestimation of statistical uncertainty in practical problems will be verified. (authors)