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Abstract:
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The search for features in signals is a common but statistically challenging problem in (astro)physics. Bumps above background can be used to identify the composition of an astronomical source and were used in the discovery of the Higgs Boson. Unexpected structure that appears in images may reveal a true source feature or simply be noise in the data. Unfortunately, existing detection methods are often dismissed because of unsatisfactory false-positives rates, the requirement of independence among the search regions, or computational costs. This talk formulates a new solution, TOHM (Testing One Hypothesis Multiple times), that formulates the problem in terms of testing with a potentially multivariate parameter that is present only under the alternative. The proposed methodology can be applied in settings outside of astrophysics and combines elements of geometry, graph theory and Monte Carlo methods with the goal of providing an easy to compute, computationally efficient and highly generalizable inferential solution.
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