Abstract
This note describes the application of Gaussian mixture regression to track fitting with a Gaussian mixture model of the position errors. The mixture model is assumed to have two components with identical component means. Under the premise that the association of each measurement to a specific mixture component is known, the Gaussian mixture regression is shown to have consistently better resolution than weighted linear regression with equivalent homoskedastic errors. The improvement that can be achieved is systematically investigated over a wide range of mixture distributions. The results confirm that with constant homoskedastic variance the gain is larger for larger mixture weight of the narrow component and for smaller ratio of the width of the narrow component and the width of the wide component.
Highlights
In the data analysis of high-energy physics experiments, and in track fitting, Gaussian models of measurements errors or Gaussian models of stochastic processes such as multiple Coulomb scattering and energy loss of electrons by bremsstrahlung may turn out to be too simplistic or downright invalid
In the application to track fitting, heteroskedastic mixture models can be useful in non-uniform tracking detectors, in which the mixture model obtained by the calibration depends on the layer or on the sensor or on the possible cluster types
The third study investigates the effect of multiple Coulomb scattering (MCS) on the results presented in the previous subsection
Summary
In the data analysis of high-energy physics experiments, and in track fitting, Gaussian models of measurements errors or Gaussian models of stochastic processes such as multiple Coulomb scattering and energy loss of electrons by bremsstrahlung may turn out to be too simplistic or downright invalid. In these circumstances Gaussian mixture models (GMMs) can be used in the data analysis to model outliers or tails in position measurements of tracks [1,2], to model the tails of the multiple Coulomb scattering distribution [3,4], or to approximate the distribution of the energy loss of electrons by bremsstrahlung [5] In these applications it is not known to which component an observation or a physical process corresponds, and it is up to the track fit via the Deterministic Annealing Filter or the Gaussian-sum Filter to determine the association probabilities [6,7,8,9].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
