A Planck-scale limit on spacetime fuzziness and stochastic Lorentz invariance violation

We give a classical confidence belt construction which unifies the treatment of upper confidence limits for null results and two-sided confidence intervals for non-null results. The unified treatment solves a problem (apparently not previously recognized) that the choice of upper limit or two-sided intervals leads to intervals which are not confidence intervals if the choice is based on the data. We apply the construction to two related problems which have recently been a battle-ground between classical and Bayesian statistics: Poisson processes with background, and Gaussian errors with a bounded physical region. In contrast with the usual classical construction for upper limits, our construction avoids unphysical confidence intervals. In contrast with some popular Bayesian intervals, our intervals eliminate conservatism (frequentist coverage greater than the stated confidence) in the Gaussian case and reduce it to a level dictated by discreteness in the Poisson case. We generalize the method in order to apply it to analysis of experiments searching for neutrino oscillations. We show that this technique both gives correct coverage and is powerful, while other classical techniques that have been used by neutrino oscillation search experiments fail one or both of these criteria.

(Abridged) The Large Area Telescope (Fermi/LAT, hereafter LAT), the primary instrument on the Fermi Gamma-ray Space Telescope (Fermi) mission, is an imaging, wide field-of-view, high-energy gamma-ray telescope, covering the energy range from below 20 MeV to more than 300 GeV. This paper describes the LAT, its pre-flight expected performance, and summarizes the key science objectives that will be addressed. On-orbit performance will be presented in detail in a subsequent paper. The LAT is a pair-conversion telescope with a precision tracker and calorimeter, each consisting of a 4x4 array of 16 modules, a segmented anticoincidence detector that covers the tracker array, and a programmable trigger and data acquisition system. Each tracker module has a vertical stack of 18 x,y tracking planes, including two layers (x and y) of single-sided silicon strip detectors and high-Z converter material (tungsten) per tray. Every calorimeter module has 96 CsI(Tl) crystals, arranged in an 8 layer hodoscopic configuration with a total depth of 8.6 radiation lengths. The aspect ratio of the tracker (height/width) is 0.4 allowing a large field-of-view (2.4 sr). Data obtained with the LAT are intended to (i) permit rapid notification of high-energy gamma-ray bursts (GRBs) and transients and facilitate monitoring of variable sources, (ii) yield an extensive catalog of several thousand high-energy sources obtained from an all-sky survey, (iii) measure spectra from 20 MeV to more than 50 GeV for several hundred sources, (iv) localize point sources to 0.3 - 2 arc minutes, (v) map and obtain spectra of extended sources such as SNRs, molecular clouds, and nearby galaxies, (vi) measure the diffuse isotropic gamma-ray background up to TeV energies, and (vii) explore the discovery space for dark matter.