Asymptotic Validity of the Bayes-Inspired Indifference Zone Procedure: The Non-Normal Known Variance Case

We consider the indifference-zone (IZ) formulation of the ranking and selection problem in which the goal is to choose an alternative with the largest mean with guaranteed probability, as long as the difference between this mean and the second largest exceeds a threshold. Conservatism leads classical IZ procedures to take too many samples in problems with many alternatives. The Bayes-inspired Indifference Zone (BIZ) procedure, proposed in Frazier (2014), is less conservative than previous procedures, but its proof of validity requires strong assumptions, specifically that samples are normal, and variances are known with an integer multiple structure. In this paper, we show asymptotic validity of a slight modification of the original BIZ procedure as the difference between the best alternative and the second best goes to zero,when the variances are known and finite, and samples are independent and identically distributed, but not necessarily normal

Higgs mediated lepton flavor violating tau decays τ→μγ\tau \to \mu \gamma and τ→μγγ\tau \to \mu \gamma \gamma in effective theories

The size of the branching ratios for the $\tau \to \mu \gamma$ and $\tau \to \mu \gamma \gamma$ decays induced by a lepton flavor violating Higgs interaction $H\tau \mu$ is studied in the frame of effective field theories. The best constraint on the $H\tau \mu$ vertex, derived from the know measurement on the muon anomalous magnetic moment, is used to impose the upper bounds $Br(\tau \to \mu \gamma)<2.5\times 10^{-10}$ and $Br(\tau \to \mu \gamma \gamma)<2.3\times 10^{-12}$, which are more stringent than current experimental limits on this class of transitions.Comment: 6 pages, 3 figure