Practical Statistics

Accelerators and detectors are expensive, both in terms of money and human effort. It is thus important to invest effort in performing a good statistical analysis of the data, in order to extract the best information from it. This series of five lectures deals with practical aspects of statistical issues that arise in typical High Energy Physics analyses.Comment: 26 pages, contribution to the CERN in the Proceedings of the 2015 CERN-Latin-American School of High-Energy Physics, Ibarra, Ecuador, 4 - 17 March 201

Inferences Concerning the Magnetospheric Source Region for Auroral Breakup

It is argued that the magnetospheric source region for auroral arc breakup and substorm initiation is along boundary plasma sheet (BPS) magnetic field lines. This source region lies beyond a distinct central plasma sheet (CPS) region and sufficiently far from the Earth that energetic ion motion violates the guiding center approximation (i.e., is chaotic). The source region is not constrained to any particular range of distances from the Earth, and substorm initiation may be possible over a wide range of distances from near synchronous orbit to the distant tail. It is also argued that the layer of low-energy electrons and velocity dispersed ion beams observed at low altitudes on Aureol 3 is not a different region from the region of auroral arcs. Both comprise the BPS. The two regions occasionally appear distinct at low altitudes because of the effects of arc field-aligned potential drops on precipitating particles

Conditions for double layers in the Earth's magnetosphere and perhaps in other astrophysical objects

Double layers form along auroral field lines in the Earth's magnetosphere. They form in order to maintain current continuity in the ionosphere in the presence of a magnetospheric electric field E with nabla x E is not equal to 0. Features which govern the formation of the double layers are: (1) the divergence of E, (2) the conductivity of the ionosphere, and (3) the current-voltage characteristics of auroral magnetic field lines. Astrophysical situations where nabla x E is not equal to 0 is applied to a conducting plasma similar to the Earth's ionosphere are potential candidates for the formation of double layers. The region with nabla x E is not equal to 0 can be generated within, or along field lines connected to, the conducting plasma. In addition to nabla x E, shear neutral flow in the conducting plasma can also form double layers

Evaluating auroral processes within a magnotospheric model

A summary of the research performed is included. Topics covered include magnetospheric model; association between discrete auroras and ion precipitation from the tail current sheet; auroral arc scale sizes and structures; polar cap size variation; low-altitude auroral boundary; auroral wave-particle interactions; thermospheric interactions; and the neutral wind 'flywheel'

Energetic and magnetosheath energy particle signatures of the low-latitude boundary layer at low altitudes near noon

The low-latitude boundary layer (LBL) and its separation from the cusp have previously been identified using observations of particle precipitation at magnetosheath energies. Using S3-3 satellite observations, we have determined that these identifications can also be made from energetic particle observations on polar-orbiting satellites. It is found that the equatorward boundary of the LBL is identifiable as an approximately discontinuous decrease in 33-keV electron fluxes from low to high latitudes. Both the energetic ion and electron fluxes decrease discontinuously at the boundary between the LBL and the cusp or polar cap. A distinct LBL is nearly always identifiable in energetic particle measurements in the 10-14 MLT region when counting rates are statistically significant. The identifications obtained using the energetic particle measurements have been compared to those obtained using criteria developed by Newell and Meng (1988, 1989) for magnetosheath energy particle precipitation. In this way, we have evaluated the accuracy of both techniques and used the energetic particle measurements to supplement the identifications obtained using the Newell and Meng criteria. We propose that the Newell and Meng threshold on ion energy flux can be reduced by a factor of 6. This modification provides identification of the LBL for lower ion intensity levels than has previously been thought possible. Source, acceleration, and scattering processes have also been studied within and in the vicinity of the LBL. Observed trapped pitch angle distributions of energetic electrons imply that the LBL is at least partially on closed field lines. Strong scattering of energetic protons is found within and equatorward of the LBL and thus must occur at least partially along closed field lines. Field-aligned electron acceleration by parallel electric fields can be discerned within and poleward of the LBL, but a more detailed analysis is necessary for a statistical study. Conical ion acceleration was seen relatively frequently within the LBL and about half as often poleward of the LBL. Neither acceleration process could be identified anywhere equatorward of the LBL

Consistency in statistical moments as a test for bubble cloud clustering

Frequency dependent measurements of attenuation and/or sound speed through clouds of gas bubbles in liquids are often inverted to find the bubble size distribution and the void fraction of gas. The inversions are often done using an effective medium theory as a forward model under the assumption that the bubble positions are Poisson distributed (i.e., statistically independent). Under circumstances in which single scattering does not adequately describe the pressure field, the assumption of independence in position can yield large errors when clustering is present, leading to errors in the inverted bubble size distribution. It is difficult, however, to determine the existence of clustering in bubble clouds without the use of specialized acoustic or optical imaging equipment. A method is described here in which the existence of bubble clustering can be identified by examining the consistency between the first two statistical moments of multiple frequency acoustic measurements

An Estimate of the Gas Transfer Rate from Oceanic Bubbles Derived from Multibeam Sonar Observations of a Ship Wake

Measurements of gas transfer rates from bubbles have been made in the laboratory, but these are difficult to extrapolate to oceanic bubbles where populations of surfactants and particulate matter that inhibit gas transfer are different. Measurements at sea are complicated by unknown bubble creation rates that make it difficult to uniquely identify and observe the evolution of individual bubble clouds. One method that eliminates these difficulties is to measure bubbles in a ship wake where bubble creation at any given location is confined to the duration of the passing ship. This method assumes that the mechanisms slowing the gas dissolution of naturally created bubbles act in a similar manner to slow the dissolution of bubbles in a ship wake. A measurement of the gas transfer rate for oceanic bubbles using this method is reported here. A high-frequency upward-looking multibeam echosounder was used to measure the spatial distribution of bubbles in the wake of a twin screw 61-m research vessel. Hydrodynamic forcing functions are extracted from the multibeam data and used in a bubble cloud evolution model in which the gas transfer rate is treated as a free parameter. The output of model runs corresponding to different gas transfer rates is compared to the time-dependent wake depth observed in the data. Results indicating agreement between the model and the data show that the gas transfer rate must be approximately 15 times less then it would be for surfactant-free bubbles in order to explain the bubble persistence in the wake

High-Precision Entropy Values for Spanning Trees in Lattices

Shrock and Wu have given numerical values for the exponential growth rate of the number of spanning trees in Euclidean lattices. We give a new technique for numerical evaluation that gives much more precise values, together with rigorous bounds on the accuracy. In particular, the new values resolve one of their questions.Comment: 7 pages. Revision mentions alternative approach. Title changed slightly. 2nd revision corrects first displayed equatio

Is the New Resonance Spin 0 or 2? Taking a Step Forward in the Higgs Boson Discovery

The observation of a new boson of mass \sim 125\gev at the CERN LHC may finally have revealed the existence of a Higgs boson. Now we have the opportunity to scrutinize its properties, determining its quantum numbers and couplings to the standard model particles, in order to confirm or not its discovery. We show that by the end of the 8 TeV run, combining the entire data sets of ATLAS and CMS, it will be possible to discriminate between the following discovery alternatives: a scalar $J^P=0^+$ or a tensor $J^P=2^+$ particle with minimal couplings to photons, at a $5\sigma$ statistical confidence level at least, using only diphotons events. Our results are based on the calculation of a center-edge asymmetry measure of the reconstructed {\it sPlot} scattering polar angle of the diphotons. The results based on asymmetries are shown to be rather robust against systematic uncertainties with comparable discrimination power to a log likelihood ratio statistic.Comment: 11 pages, 6 figures, 1 table. References added, minor typos correcte