Application of Importance Sampling for Point Source Analysis with the IceCube Neutrino Observatory

Abstract

The IceCube Neutrino Observatory observes astrophysical neutrinos produced by the most energetic processes in the Universe. To date, the exact sources of these neutrinos, particles with no electric charge and almost negligible mass, are still a mystery. In an attempt to identify the sources of the highest energy neutrinos, the IceCube Collaboration uses likelihood analysis to search for clustering of neutrino events in the sky. An important part of this analysis is knowing how often neutrinos randomly cluster on the sky to replicate what an astrophysical neutrino source would look like. However, numerous simulations are required to properly understand this, and hence so are excessive computational resources. In this thesis, importance sampling is used to force rare clusters of neutrinos to occur on simulated skies. Two methods of importance sampling have been created to force these clusters to occur, a Gaussian weighting method and a binomial weighting method. Once these events are clustered, an appropriate weight can be applied to the sky the cluster is created on, and a likelihood analysis can be performed. We demonstrate how these methods can be used to identify the frequency at which rare clusterings of neutrinos occur, without the requirement of exhaustive computational time. We find that these rare clusters can be forced to occur on a sky with importance sampling, as can appropriate weights indicating the frequency the cluster would appear at a fixed point in space. However, further investigation is required to understand how to correctly apply sampling weights to the results when we perform the likelihood analysis over a full sky. The result of using importance sampling to identify rare clusters of neutrinos is used to investigate the effectiveness of a new test statistic for hypothesis testing in point source analysis. The most powerful test statistic for this analysis is the maximum likelihood, ℒ.̂ This is obtained by maximising a likelihood function relative to the maximum number of signal events, 𝑛̂𝑠, from some position on the sky. We construct a new statistic using a combination of the ℒ̂ and 𝑛̂𝑠 values, which has been suggested to be a more powerful test statistic than ℒ̂on its own. Using distributions obtained with importance sampling, we find that there is no evidence to indicate that a test statistic constructed using ℒ̂and 𝑛̂𝑠 is more powerful than ℒ̂on its own. Furthermore, we find that it simply replicates the results of ℒ̂by itself, due to the strong correlation between the ℒ̂and 𝑛̂𝑠 combinations in the null and alternate hypotheses tested.