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Gaussian Process vs. Log Gaussian Cox Process: Comparing Methods for High Energy Physics Data

POSTER

Abstract

High energy physics (HEP) data from particle colliders are studied using statistical methods to compare the data we observe with what we expect. HEP collider data is often arranged into histograms of counts of the number of events observed with a given feature value which can be modeled with the Poisson distribution. In many analyses, the signal appears as a localized excess on top of a smooth background that must be modeled to observe a signal. For this project, we use toy data that mimics the falling exponential behavior of HEP data. An effective method for modeling smooth backgrounds in HEP data are Gaussian processes. Nonetheless, this method requires data to be binned, which loses information. Gaussian processes generally yield meaningful uncertainties, but it fails to capture the Poissonian uncertainties of HEP data. The log Gaussian Cox process is a novel method we expect to improve on those shortcomings. We compare the ability of the Gaussian process and the log Gaussian Cox process to reproduce a known intensity function when modeling the smooth background events. We find that the log Gaussian Cox process is promising, however, further exploration is needed to create an optimal model and develop a deeper understanding of the log Gaussian Cox process.

Authors

  • Pavani Jairam

    Duke University

  • Kristin Rabosky

    Middle Tennessee State University, University of Alabama Tuscaloosa, Swarthmore College, CT Clinical Innovation Center, Department of Radiology, Mayo Clinic, Rochester, MN, Bard College, Wright State University, University of Michigan, University of Hawai'i-Manoa, Rice University, University of Alaska Fairbanks, University of Utah, South Dakota School of Mines and Technology, Furman University, University of Notre Dame, Theoretical Physics Division, Institute of High Energy Physics, the Chinese Academy of Sciences, Peng Huanwu Center for Fundamental Theory, University of Science and Technology China, University of Cambridge, University of Kansas, SLAC National Accelerator Laboratory, Planetary Science Institute, Iowa State University, College of Idaho, University of Washington, Bothell, Ottawa Hills High School, Case Western Reserve University, Yale University and Strasbourg Astronomical Observatory, Yale University, Korea Astronomy and Space Science Institute, NOIRLab, Purdue University, Korea Instotute for Advanced Study, Perimeter Institute, Rutgers University, University of Maryland, Juniata College, Columbia University, City University of New York / American Museum of Natural History, Columbia University / American Museum of Natural History, Morehead State University, Hofstra University, Occidental College, Georgia Institute of Technology, School of Physics and Astronomy, University of Minnesota, The Oskar Klein Centre, Department of Astronomy, University of Mississippi, Stanford/KIPAC/SLAC, University of Connecticut, Kansas State University, Vassar College, Penn State, Department of Chemistry and Biochemistry, Worcester Polytechnic Institute, Department of Physics, Worcester Polytechnic Institute, Clark University, University of Illinois at Urbana-Champaign, Rhodes College, Rensselaer Polytechnic Institute, Harvard University, Cornell University, Air Force Research Lab, Wright-Patterson AFB, Ohio 45433, Air Force Research Lab, Wright-Patterson AFB, Ohio 45433 & UES, Inc., 4401 Dayton-Xenia Rd, Dayton, OH 45432, Department of Physics, University of Dayton, Dayton Ohio & Air Force Research Lab, Wright-Patterson AFB, Ohio 45433, Los Alamos National Laboratory, Utah State University, Ramapo College of NJ, Brookhaven National Laboratory, Research Center of Topological Functional Materials and Henan Key Laboratory of Photovoltaic Materials, Henan Univers., Brookhaven National Laboratory, Montclair State University, Weber State University

  • Kristin Rabosky

    Middle Tennessee State University, University of Alabama Tuscaloosa, Swarthmore College, CT Clinical Innovation Center, Department of Radiology, Mayo Clinic, Rochester, MN, Bard College, Wright State University, University of Michigan, University of Hawai'i-Manoa, Rice University, University of Alaska Fairbanks, University of Utah, South Dakota School of Mines and Technology, Furman University, University of Notre Dame, Theoretical Physics Division, Institute of High Energy Physics, the Chinese Academy of Sciences, Peng Huanwu Center for Fundamental Theory, University of Science and Technology China, University of Cambridge, University of Kansas, SLAC National Accelerator Laboratory, Planetary Science Institute, Iowa State University, College of Idaho, University of Washington, Bothell, Ottawa Hills High School, Case Western Reserve University, Yale University and Strasbourg Astronomical Observatory, Yale University, Korea Astronomy and Space Science Institute, NOIRLab, Purdue University, Korea Instotute for Advanced Study, Perimeter Institute, Rutgers University, University of Maryland, Juniata College, Columbia University, City University of New York / American Museum of Natural History, Columbia University / American Museum of Natural History, Morehead State University, Hofstra University, Occidental College, Georgia Institute of Technology, School of Physics and Astronomy, University of Minnesota, The Oskar Klein Centre, Department of Astronomy, University of Mississippi, Stanford/KIPAC/SLAC, University of Connecticut, Kansas State University, Vassar College, Penn State, Department of Chemistry and Biochemistry, Worcester Polytechnic Institute, Department of Physics, Worcester Polytechnic Institute, Clark University, University of Illinois at Urbana-Champaign, Rhodes College, Rensselaer Polytechnic Institute, Harvard University, Cornell University, Air Force Research Lab, Wright-Patterson AFB, Ohio 45433, Air Force Research Lab, Wright-Patterson AFB, Ohio 45433 & UES, Inc., 4401 Dayton-Xenia Rd, Dayton, OH 45432, Department of Physics, University of Dayton, Dayton Ohio & Air Force Research Lab, Wright-Patterson AFB, Ohio 45433, Los Alamos National Laboratory, Utah State University, Ramapo College of NJ, Brookhaven National Laboratory, Research Center of Topological Functional Materials and Henan Key Laboratory of Photovoltaic Materials, Henan Univers., Brookhaven National Laboratory, Montclair State University, Weber State University