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Abstract:
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The question of how best to select among models has bedeviled statisticians, particularly Bayesian statisticians, for decades. The difficulties with interpreting p-values are well known among Bayesians and non-Bayesians alike. Unfortunately, the strong dependence on the choice of prior distribution of the most prominent fully Bayesian alternative, the Bayes Factor, has limited its popularity in practice. In this poster, we explore a class of non-standard model comparison problems that are important in astrophysics and high-energy physics. The search for the Higgs boson, for example, involved quantifying evidence for a narrow component added to a diffuse background distribution. The added component corresponds to the Higgs mass distribution, accounting for instrumental effects, and cannot be negative. Thus, not only is the null distribution on the boundary of the parameter space, but the location of the added component is unidentifiable under the null. We discuss how this can be formulated as a multiple testing problem and compare the resulting p-value with Bayes Factors. In this case, the prior dependence of the Bayes Factor results in a natural correction for the multiple testing.
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