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In $662$ live days during 2010–2012, $28$ events exceeded the expected $10.6_{-3.6}^{+5.0}$ atmospheric events. Energy, direction and topology supported an extraterrestrial component. Combined searches gave $4.1\sigma$ with additional benchmark charm background; uncertain charm production affected significance. No source clustering was established.^[ref]

A diffuse excess and an identified source answer different questions. The first compares populations against a background hypothesis; the second needs an association in direction, perhaps also in time.

Escaping muons or neutrinos can make deposited energy smaller than incoming neutrino energy.^[ref]

The 2013 selection rejected early boundary light. Tagged muons checked leakage; air shower companion muons also vetoed downward atmospheric neutrinos.^[ref]

A simple original conditional probability model explains why a veto changes the selected mixture. Let $A$ mean that an atmospheric neutrino interaction would pass all other cuts, $M$ that an accompanying muon reaches the veto, and $V$ that the veto fires. Set $a=P(M\mid A)$ and $ϵ=P(V\mid M,A)$, and neglect unrelated veto hits. The law of total probability givesFor chosen $a=0.8$ and $ϵ=0.95$, the passing fraction is $0.24$. Neither this value nor either input is an IceCube measurement. With equal incident candidate populations, this mechanism alone reduces the atmospheric contribution relative to a hypothetical population having $a=0$. It does not make every surviving event astronomical: $a=0$ or $ϵ=0$ gives no suppression, while $a=ϵ=1$ removes the entire chosen atmospheric population. If unrelated light vetoes a surviving event independently with probability $u$, its passing fraction becomes $(1-u)(1-aϵ)$; independence is an additional assumption.