A novel approach for pre-filtering event sources using the von Mises–Fisher distribution

Searching for as yet undetected γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\gamma $\end{document}-ray sources is one of the main stated goals of the Fermi Large Area Telescope Collaboration. In this paper, we explore the capability of a filtering method based on a finite mixture of von Mises–Fisher distributions. The proposed procedure is specifically designed to handle data with support on the unit sphere. The assumption of a parametric model for each high energy emitting source allows us to derive an explicit expression for both the direction of the sources and their angular resolutions. The corresponding measures are based on the directional mean and the quantiles of the single mixture components. Sound criteria of model selection can provide an automatic way to determine the number of detected sources. Additionally, a likelihood-ratio test is developed to evaluate their significance. The procedure is tested on simulated data sets of photon emissions from high energy sources within the energy range [10−1,000] GeV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[10 - 1,000]\text{ GeV}$\end{document}. A real data example consisting of a sample of the Fermi LAT data collected over a period of about 7.2 years within the energy range [10−1,000] GeV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[10 - 1,000]\text{ GeV}$\end{document}, in a subregion of the γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\gamma $\end{document}-ray sky, is furthermore provided.