Frequentist and Bayesian confidence intervals

Frequentist (classical) and Bayesian approaches to the construction of confidence limits are compared. Various examples which illustrate specific problems are presented. The Likelihood Principle and the Stopping Rule Paradox are discussed. The performance of the different methods is investigated relative to the properties coherence, precision, bias, universality, simplicity. A proposal on how to define error limits in various cases are derived from the comparison. They are based on the likelihood function only and follow in most cases the general practice in high energy physics. Classical methods are not recommended because they violate the Likelihood Principle, they can produce inconsistent results, suffer from lack of precision and generality. Also the extreme Bayesian approach with arbitrary choice of the prior probability density or priors deduced from scaling laws is rejected.     

Fast and accurate X‐ray fluorescence computed tomography imaging with the ordered‐subsets expectation maximization algorithm

The ordered‐subsets expectation maximization algorithm (OSEM) is introduced to X‐ray fluorescence computed tomography (XFCT) and studied; here, simulations and experimental results are presented. The simulation results indicate that OSEM is more accurate than the filtered back‐projection algorithm, and it can efficiently suppress the deterioration of image quality within a large range of angular sampling intervals. Experimental results of both an artificial phantom and cirrhotic liver show that with a satisfying image quality the angular sampling interval could be improved to save on the data‐acquisition time when OSEM is employed. In addition, with an optimum number of subsets, the image reconstruction time of OSEM could be reduced to about half of the time required for one subset. Accordingly, it can be concluded that OSEM is a potential method for fast and accurate XFCT imaging.     

Tests and characterization of a laterally graded multilayer Montel mirror

Multilayers are becoming an increasingly important tool in X‐ray optics. The essential parameters to design a pair of laterally graded multilayer mirrors arranged in a Montel‐type configuration for use as an X‐ray collimating device are provided. The results of X‐ray reflectometry tests carried out on the optics in addition to metrology characterization are also shown. Finally, using experimental data and combined with X‐ray tracing simulations it is demonstrated that the mirror meets all stringent specifications as required for a novel ultra‐high‐resolution inelastic X‐ray scattering spectrometer at the Advanced Photon Source.     

Uncertainty estimation in seismo-acoustic reflection travel time inversion

This paper develops a nonlinear Bayesian inversion for high-resolution seabed reflection travel time data including rigorous uncertainty estimation and examination of statistical assumptions. Travel time data are picked on seismo-acoustic traces and inverted for a layered sediment sound-velocity model. Particular attention is paid to picking errors which are often biased, correlated, and nonstationary. Non-Toeplitz data covariance matrices are estimated and included in the inversion along with unknown travel time offset (bias) parameters to account for these errors. Simulated experiments show that neglecting error covariances and biases can cause misleading inversion results with unrealistically high confidence. The inversion samples the posterior probability density and provides a solution in terms of one- and two-dimensional marginal probability densities, correlations, and credibility intervals. Statistical assumptions are examined through the data residuals with rigorous statistical tests. The method is applied to shallow-water data collected on the Malta Plateau during the SCARAB98 experiment.     

The effect of oil on the performance of heat pumps and refrigerators—II. Experimental results

The results of a prolonged investigation of the influence of the lubricating oil Shell Clavus 68 on the performance of an R12-based refrigeration-heat pump system are presented. The strategy is discussed for deciding if a given series of data collected at 10s intervals adequately represents the chosen experimental conditions and results are presented under both transient and steady state conditions. The effects of oil on evaporator capacity, coefficient of performance, heat transfer rates, evaporator outlet superheat stability, refrigerant mass flow rate, evaporator pressure drop and compressor discharge temperature are discussed, and the experimental results are compared with a theoretical analysis. Finally, it is shown that under certain (albeit unlikely) conditions, it is possible for both the evaporator and condensor to act as heat rejectors.     

Artificial neural networks applied to the analysis of synchrotron nuclear resonant scattering data

The capabilities of artificial neural networks (ANNs) have been investigated for the analysis of nuclear resonant scattering (NRS) data obtained at a synchrotron source. The major advantage of ANNs over conventional analysis methods is that, after an initial training phase, the analysis is fully automatic and practically instantaneous, which allows for a direct intervention of the experimentalist on‐site. This is particularly interesting for NRS experiments, where large amounts of data are obtained in very short time intervals and where the conventional analysis method may become quite time‐consuming and complicated. To test the capability of ANNs for the automation of the NRS data analysis, a neural network was trained and applied to the specific case of an Fe/Cr multilayer. It was shown how the hyperfine field parameters of the system could be extracted from the experimental NRS spectra. The reliability and accuracy of the ANN was verified by comparing the output of the network with the results obtained by conventional data analysis.     

SEMI-INCL USIVE DISTRIBUTIONS AND RAPIDITY DEPENDENCE OF MULTIPLICITY DISTRIBUTIONS IN e+e－ ANNIHILATION INTO TWO JETS

In this paper,the rapidity distribution of quarks is further assumed to be a uniform distribution with the constraint of four momentum conservation.We apply Monte Carlo approaches to light quark jets.The semi-inclusive distributions and the multiplicity distributions in rapidity intervals are calculated.The characteristics of these distributions are discussed and the results are compared with the experimental data of average jets.     

Temperature dependence of the hyperfine parameters of the iron bearing phases in the Mössbauer spectra collected by the Mars Exploration Rover Spirit

This contribution focuses on the Mössbauer spectra acquired by the Mars Exploration Rover Spirit which carried a MIMOS II Mössbauer spectrometer. Only those spectra which present a reasonable statistical quality were selected to for this study. Twenty five Mössbauer spectra have been considered. Common phases identified from the temperature dependent hyperfine parameters are olivine, pyroxene, hematite and magnetite. It is believed that the applied analysis method has provided accurate values for the various hyperfine data averaged over single 10 K temperature intervals in the range 210–260 K. The obtained results, to some extent forced to evolve consistently over the various ΔT intervals considered for a given soil/rock target, are in many cases different from previously published data. Possible reasons for these differences will be discussed.     

High‐performance X‐ray detectors for the new powder diffraction beamline I11 at Diamond

The design and performance characterization of a new light‐weight and compact X‐ray scintillation detector is presented. The detectors are intended for use on the new I11 powder diffraction beamline at the third‐generation Diamond synchrotron facility where X‐ray beams of high photon brightness are generated by insertion devices. The performance characteristics of these detection units were measured first using a radioactive source (efficiency of detection and background count rate) and then synchrotron X‐rays (peak stability, light yield linearity and response consistency). Here, the results obtained from these tests are reported, and the suitability of the design for the Diamond powder beamline is demonstrated by presenting diffraction data obtained from a silicon powder standard using a prototype multicrystal analyser stage.     

An assessment of large eddy simulations of premixed flames propagating past repeated obstacles

This paper presents an assessment of Large Eddy Simulations (LES) in calculating the structure of turbulent premixed flames propagating past solid obstacles. One objective of the present study is to evaluate the LES simulations and identify the drawbacks in accounting the chemical reaction rate. Another objective is to analyse the flame structure and to calculate flame speed, generated overpressure at different time intervals following ignition of a stoichiometric propane/air mixture. The combustion chamber has built-in repeated solid obstructions to enhance the turbulence level and hence increase the flame propagating speed. Various numerical tests have also been carried out to determine the regimes of combustion at different stages of the flame propagation. These have been identified from the calculated results for the flow and flame characteristic parameters. It is found that the flame lies within the ‘thin reaction zone’ regime which supports the use of the laminar flamelet approach for modelling turbulent premixed flames. A submodel to calculate the model coefficient in the algebraic flame surface density model is implemented and examined. It is found that the LES predictions are slightly improved owing to the calculation of model coefficient by using submodel. Results are presented and discussed in this paper are for the flame structure, position, speed, generated pressure and the regimes of combustion during all stages of flame propagation from ignition to venting. The calculated results are validated against available experimental data.     

Asymptotic formulae for likelihood-based tests of new physics

We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow one to account for systematic uncertainties. Explicit formulae for the asymptotic distributions of test statistics are derived using results of Wilks and Wald. We motivate and justify the use of a representative data set, called the “Asimov data set”, which provides a simple method to obtain the median experimental sensitivity of a search or measurement as well as fluctuations about this expectation.     

Speckle velocimeter for a self-powered vehicle

Laboratory tests of a laser speckle velocimetry technique are reported. The use of integral statistics in the space-time plane is discussed. Preliminary experimental results are compared with data obtained by other speckle velocimeter methods.     

An X‐ray Raman spectrometer for EXAFS studies on minerals: bent Laue spectrometer with 20 keV X‐rays

An X‐ray Raman spectrometer for studies of local structures in minerals is discussed. Contrary to widely adopted back‐scattering spectrometers using ≤10 keV X‐rays, a spectrometer utilizing ～20 keV X‐rays and a bent Laue analyzer is proposed. The 20 keV photons penetrate mineral samples much more deeply than 10 keV photons, so that high intensity is obtained owing to an enhancement of the scattering volume. Furthermore, a bent Laue analyzer provides a wide band‐pass and a high reflectivity, leading to a much enhanced integrated intensity. A prototype spectrometer has been constructed and performance tests carried out. The oxygen K‐edge in SiO₂ glass and crystal (α‐quartz) has been measured with energy resolutions of 4 eV (EXAFS mode) and 1.3 eV (XANES mode). Unlike methods previously adopted, it is proposed to determine the pre‐edge curve based on a theoretical Compton profile and a Monte Carlo multiple‐scattering simulation before extracting EXAFS features. It is shown that the obtained EXAFS features are reproduced fairly well by a cluster model with a minimal set of fitting parameters. The spectrometer and the data processing proposed here are readily applicable to high‐pressure studies.     

Development and exploration of a new methodology for the fitting and analysis of XAS data

A new data analysis methodology for X‐ray absorption near‐edge spectroscopy (XANES) is introduced and tested using several examples. The methodology has been implemented within the context of a new Matlab‐based program discussed in a companion related article [Delgado‐Jaime et al. (2010), J. Synchrotron Rad. 17 , 132–137]. The approach makes use of a Monte Carlo search method to seek appropriate starting points for a fit model, allowing for the generation of a large number of independent fits with minimal user‐induced bias. The applicability of this methodology is tested using various data sets on the Cl K‐edge XAS data for tetragonal CuCl₄^2?, a common reference compound used for calibration and covalency estimation in M—Cl bonds. A new background model function that effectively blends together background profiles with spectral features is an important component of the discussed methodology. The development of a robust evaluation function to fit multiple‐edge data is discussed and the implications regarding standard approaches to data analysis are discussed and explored within these examples.     

Baryon spin-parity tests using polarized proton targets or beams

A new method is proposed for performing combined spin and parity tests on baryon resonances generated in quasi-two-body production experiments, without any dynamical hypothesis, using polarized proton targets or beams. These tests present the advantage of being applicable to data averaged over intervals of momentum transfer and mass. In order to estimate the sensitivity of the tests to experimental errors, a simulated experiment with random errors is analysed, and quite good stability is found.     

An Orbital‐Free Quantum Hypernetted Chain Model Based Perturbation Theory for Equation of State of Hydrogen and Helium in Warm Dense Regime

We present in this work, a thermodynamic perturbation theory for equation of state of hydrogen and helium in the warm dense regime. The system is modeled as a mixture of classical point ions and quantum electrons. A perturbation series for Helmholtz free energy and correlation functions of the ions and electrons as a function of density and temperature is proposed. Combining the classical thermodynamic perturbation theory and the orbitial‐free quantum hyper‐netted chain theory, a systematic procedure to obtain the terms of the perturbation series is developed. The ion‐ion correlations are treated within the hyper‐netted chain approximation and the ion‐electron correlations are treated within the Thomas‐Fermi‐Dirac‐Weizsäcker approximation. The method has been applied to obtain isotherms of hydrogen and helium in the warm dense regime. The isotherms are compared with available ab‐initio data and the results are analyzed. A good agreement with ab‐initio data has been observed for pressures greater than one Mbar. Advantages and limitations of the present method are discussed along with possible future improvements. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the 40th anniversary of the journal X‐Ray Spectrometry

This journal, X‐Ray Spectrometry, celebrates its 40th anniversary this year. The state of the publications on X‐ray spectral analysis from 1972 onward is considered. The distribution of materials over countries is presented, as published in X‐Ray Spectrometry for 40 years, in 5‐year time intervals: 1972–1976, 1977–1981, and so on. The participation of Russian scientists contributing to the publications in this journal is discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Comparison between volatility return intervals of the S&;P 500 index and two common models

We analyze the S&P 500 index data for the 13-year period, from January 1, 1984 to December 31, 1996, with one data point every 10 min. For this database, we study the distribution and clustering of volatility return intervals, which are defined as the time intervals between successive volatilities above a certain threshold q. We find that the long memory in the volatility leads to a clustering of above-median as well as below-median return intervals. In addition, it turns out that the short return intervals form larger clusters compared to the long return intervals. When comparing the empirical results to the ARMA-FIGARCH and fBm models for volatility, we find that the fBm model predicts scaling better than the ARMA-FIGARCH model, which is consistent with the argument that both ARMA-FIGARCH and fBm capture the long-term dependence in return intervals to a certain extent, but only fBm accounts for the scaling. We perform the Student's t-test to compare the empirical data with the shuffled records, ARMA-FIGARCH and fBm. We analyze separately the clusters of above-median return intervals and the clusters of below-median return intervals for different thresholds q. We find that the empirical data are statistically different from the shuffled data for all thresholds q. Our results also suggest that the ARMA-FIGARCH model is statistically different from the S&P 500 for intermediate q for both above-median and below-median clusters, while fBm is statistically different from S&P 500 for small and large q for above-median clusters and for small q for below-median clusters. Neither model can fully explain the entire regime of q studied.     

XAFS analysis of indium oxynitride thin films grown on silicon substrates

Local structure of indium oxynitride thin films grown on silicon substrates was investigated by X‐ray absorption fine structure technique incorporated with first principle calculations. The thin films were grown by using reactive gas timing radio frequency (RF) magnetron sputtering technique with nitrogen (N₂) and oxygen (O₂) as reactive gasses. The reactive gasses were interchangeably fed into sputtering system at five different time intervals. The gas feeding time intervals of N₂:O₂ are 30 : 0, 30 : 5, 30 : 10, 30 : 20 and 10 : 30 s, respectively. The analysis results can be divided into three main categories. Firstly, the films grown with 30 : 0 and 30 : 5 s gas feeding time intervals are wurtzite structure indium nitride with 25 and 43% oxygen contaminations, respectively. Secondary, the film grown with 10 : 30 s gas feeding time intervals is bixbyite structure indium oxide. Finally, the films are alloying between indium nitride and indium oxide for other growth condition. The fitted radial distribution spectra, the structural parameters and the combination ratios of the alloys are discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Hadron multiplicities

We review results on hadron multiplicities in high-energy particle collisions. Both theory and experiment are discussed. The general procedures used to describe particle multiplicity in quantum chromodynamics (QCD) are summarized. The QCD equations for the generating functions of the multiplicity distributions are presented both for fixed and running coupling strengths. The mean multiplicities of gluon and quark jets, their ratio, higher moments, and the slopes of multiplicities as a function of energy scale, are among the main global features of multiplicity for which QCD results exist. Recent data from high energy e⁺e⁻ experiments, including results for separated quark and gluon jets, allow rather direct tests of these results. The theoretical predictions are generally quite successful when confronted with data. Jet and subjet multiplicities are described. Multiplicity in limited regions of phase space is discussed in the context of intermittency and fractality. The problem of singularities in the generating functions is formulated. Some special features of average multiplicities in heavy quark jets are described.