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arXiv · 2609.11683

Bayesian Superiority in On/Off analysis

Gleb Babenov·Petr Satunin
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Abstract

We present a detailed comparison of Bayesian criteria with three non-informative priors - flat, Jeffreys, and scale-invariant - for testing a signal against an unknown background and compare them with the classical frequentist Li-Ma approach in the On/Off problem. We perform Monte Carlo simulations for various background levels and evaluate the Li-Ma and Bayesian criteria by their Type I error rates. We then simulate a nonzero signal and compare the criteria in terms of Type II error rates. We find that both the Li-Ma criterion and the Bayesian criterion with the Jeffreys prior control Type I error well, excluding the case of small background $b < 0.5$; the Bayesian criterion with the Jeffreys prior is statistically more powerful than the Li-Ma criterion for $b \lesssim 40$.

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Gleb Babenov, Petr Satunin. 2026-09-17. Bayesian Superiority in On/Off analysis. https://arxiv.org/abs/2609.11683

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