GollumFit: An IceCube Open-Source Framework for Binned-Likelihood Neutrino Telescope Analyses

TL;DR

GollumFit, a framework designed for performing binned-likelihood analyses on neutrino telescope data, uniquely incorporates the particular model parameters necessary for neutrino telescopes, and solves an associated likelihood problem in a time-efficient manner.

Abstract

We present GollumFit, a framework designed for performing binned-likelihood analyses on neutrino telescope data. GollumFit incorporates model parameters common to any neutrino telescope and also model parameters specific to the IceCube Neutrino Observatory. We provide a high-level overview of its key features and how the code is organized. We then discuss the performance of the fitting in a typical analysis scenario, highlighting the ability to fit over tens of nuisance parameters. We present some examples showing how to use the package for likelihood minimization tasks. This framework uniquely incorporates the particular model parameters necessary for neutrino telescopes, and solves an associated likelihood problem in a time-efficient manner.

Figures (5)

• Figure 1: Left: a plot of the binned Monte Carlo event distribution, binned in the space of reconstructed log energy ($\log_{10}(E / \text{GeV})$) and the cosine of the reconstructed zenith angle ($\cos\theta$). The color scale indicates the number $N$ of events in each bin. To generate this distribution, all nuisance parameters are held at their prior central value. Right: in contrast, a pull plot that compares another Monte Carlo event distribution with the one on the left, assuming the prior central values of all nuisance parameters, with the exception of DOMEfficiency, which has been increased by two times its prior width. The color scale indicates the pull value comparing a new bin count $N_{+2\sigma}$ with $N$. The deficit in the bottom rows of the pull plot is due to the DOMEfficiency shifting lower energy events to higher energies, and these rows contain the lowest energy events in the sample.
• Figure 2: Overview of GollumFit. This illustration shows the main components of the main GollumFit object, the necessary inputs, and the most useful functions for analysis purposes.
• Figure 3: The result of minimization for a single fit, comparing the best-fit and initial value of the nuisance parameters, using $\sigma$, the number of prior standard deviations away from the prior value. The parameter astroPivot has a uniform prior, and no influence on the shape of the flux, and therefore little effect on the likelihood. Hence there is no preferred value to be recovered. A value of $k=0.25$ was used for the FastMC in this fit.
• Figure 4: Plot of time per likelihood evaluation as function of the number MC events looped over (corresponding to the size of the FastMC file). For reference, the total MC dataset, before the FastMC compression, consists of 13,061,947 events.
• Figure 5: Plot of the time taken for a fit (with identical seed nuisance parameters) to converge. Different bars are for different sets of nuisance parameters turned off. The number of remaining nuisance parameters fitted over is given in the parenthesis. This was performed using 814847 Monte Carlo events, after the FastMC procedure, using a value of $k=0.25$.