arXiv subjects

Rudolf Frühwirth

Publications and source records attributed to Rudolf Frühwirth.

6 recordsLinked to original sources

arXiv2023

Statistical analysis of event classification in experimental data

The paper addresses general aspects of experimental data analysis, dealing with the separation of ``signal vs. background''. It consists of two parts. Part I is a tutorial on statistical event classification, Bayesian inference, and test optimization. Aspects of the base data sample if being created by Poisson processes are discussed, and a method for estimating the unknown numbers of signal and background events is presented. Data quality of the selected events sample is assessed by the expected purity and background contamination. Part II contains a rigorous statistical analysis of the methods discussed in Part I. Both Bayesian and frequentist estimators of the unknown signal/background content are investigated. The estimates and their stochastic uncertainties are calculated for various conjugate priors in the Bayesian case, and for three choices of the virtual parent population in the frequentist case.

physics.data-an↗

arXiv2021

A new discrete distribution arising from a generalised random game and its asymptotic properties

The rules of a game of dice are extended to a "hyper-die" with $n\in\mathbb{N}$ equally probable faces, numbered from 1 to $n$. We derive recursive and explicit expressions for the probability mass function and the cumulative distribution function of the gain $G_n$ for arbitrary values of $n$. A numerical study suggests the conjecture that for $n \to \infty$ the expectation of the scaled gain $\mathbb{E}[H_n]=\mathbb{E}[G_n/\sqrt{n}\,]$ converges to $\sqrt{π/\,2}$. The conjecture is proved by deriving an analytic expression of the expected gain $\mathbb{E}[G_n]$. An analytic expression of the variance of the gain $G_n$ is derived by a similar technique. Finally, it is proved that $H_n$ converges weakly to the Rayleigh distribution with scale parameter~1.

math.PR↗

arXiv2015

A z-Vertex Trigger for Belle II

The Belle II experiment will go into operation at the upgraded SuperKEKB collider in 2016. SuperKEKB is designed to deliver an instantaneous luminosity $\mathcal{L}=8\times10^{35}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}$. The experiment will therefore have to cope with a much larger machine background than its predecessor Belle, in particular from events outside of the interaction region. We present the concept of a track trigger, based on a neural network approach, that is able to suppress a large fraction of this background by reconstructing the $z$ (longitudinal) position of the event vertex within the latency of the first level trigger. The trigger uses the hit information from the Central Drift Chamber (CDC) of Belle II within narrow cones in polar and azimuthal angle as well as in transverse momentum ("sectors"), and estimates the $z$-vertex without explicit track reconstruction. The preprocessing for the track trigger is based on the track information provided by the standard CDC trigger. It takes input from the 2D track finder, adds information from the stereo wires of the CDC, and finds the appropriate sectors in the CDC for each track. Within the sector, the $z$-vertex is estimated by a specialized neural network, with the drift times from the CDC as input and a continuous output corresponding to the scaled $z$-vertex. The neural algorithm will be implemented in programmable hardware. To this end a Virtex 7 FPGA board will be used, which provides at present the most promising solution for a fully parallelized implementation of neural networks or alternative multivariate methods. A high speed interface for external memory will be integrated into the platform, to be able to store the $\mathcal{O}(10^9)$ parameters required. The contribution presents the results of our feasibility studies and discusses the details of the envisaged hardware solution.

physics.ins-det↗

arXiv2015

A neural network z-vertex trigger for Belle II

We present the concept of a track trigger for the Belle II experiment, based on a neural network approach, that is able to reconstruct the z (longitudinal) position of the event vertex within the latency of the first level trigger. The trigger will thus be able to suppress a large fraction of the dominating background from events outside of the interaction region. The trigger uses the drift time information of the hits from the Central Drift Chamber (CDC) of Belle II within narrow cones in polar and azimuthal angle as well as in transverse momentum (sectors), and estimates the z-vertex without explicit track reconstruction. The preprocessing for the track trigger is based on the track information provided by the standard CDC trigger. It takes input from the 2D ($r - φ$) track finder, adds information from the stereo wires of the CDC, and finds the appropriate sectors in the CDC for each track in a given event. Within each sector, the z-vertex of the associated track is estimated by a specialized neural network, with a continuous output corresponding to the scaled z-vertex. The input values for the neural network are calculated from the wire hits of the CDC.

physics.ins-det↗

arXiv2012

Forward Tracking in the ILD Detector

The reconstruction software for ILD is currently subject to a major revision, aiming at improving its accuracy, speed, efficiency and maintainability in time for the upcoming DBD Report. This requires replacing old code by novel methods for track search and fit, together with modern standards for interfaces and tools. Track reconstruction in the "forward region", defined by the silicon Forward Tracking Detector (FTD), relies heavily on a powerful stand-alone track search. The new software makes use of a Cellular Automaton, a Kalman filter, and a Hopfield Neural Network. We give an overview of the project, its methods and merits.

physics.data-an↗

arXiv2010

Redescending M-estimators and Deterministic Annealing, with Applications to Robust Regression and Tail Index Estimation

A new type of redescending M-estimators is constructed, based on data augmentation with an unspecified outlier model. Necessary and sufficient conditions for the convergence of the resulting estimators to the Hubertype skipped mean are derived. By introducing a temperature parameter the concept of deterministic annealing can be applied, making the estimator insensitive to the starting point of the iteration. The properties of the annealing M-estimator as a function of the temperature are explored. Finally, two applications are presented. The first one is the robust estimation of interaction vertices in experimental particle physics, including outlier detection. The second one is the estimation of the tail index of a distribution from a sample using robust regression diagnostics.

stat.ME↗