Confronting classical and Bayesian confidence limits to examples

Classical confidence limits are compared to Bayesian error bounds by studying relevant examples. The performance of the two methods is investigated relative to the properties coherence, precision, bias, universality, simplicity. A proposal to define error limits in various cases is derived from the comparison. It is based on the likelihood function only and follows in most cases the general practice in high energy physics. Classical methods are discarded because they violate the likelihood principle, they can produce physically inconsistent results, suffer from a 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.Comment: 16 pages, 12 figure

Statistics of weighted Poisson events and its applications

The statistics of the sum of random weights where the number of weights is Poisson distributed has important applications in nuclear physics, particle physics and astrophysics. Events are frequently weighted according to their acceptance or relevance to a certain type of reaction. The sum is described by the compound Poisson distribution (CPD) which is shortly reviewed. It is shown that the CPD can be approximated by a scaled Poisson distribution (SPD). The SPD is applied to parameter estimation in situations where the data are distorted by resolution effects. It performs considerably better than the normal approximation that is usually used. A special Poisson bootstrap technique is presented which permits to derive confidence limits for observations following the CPD.Comment: 14 pages, 2 figure

An optical readout for a fibre tracker

The performance of 16 and 64 channel photomultipliers coupled to scintillating fibres has been tested. The devices are sensitive to single photoelectrons, show little gain losses for magnetic fields up to 100 Gauss and have moderate optical cross-talk. The maximum channel to channel gain variations reach a factor two for the 16 channel version and a factor of four for the 64 channel PM. The measurements and simulations indicate that the photomultipliers are well suited for the light detection in fibre trackers.Comment: 11 pages, 9 picture

Holographic optical elements: Fabrication and testing

The basic properties and use of holographic optical elements were investigated to design and construct wide-angle, Fourier-transform holographic optical systems for use in a Bragg-effect optical memory. The performance characteristics are described along with the construction of the holographic system