mfb said:
The supplementary materials are not behind a paywall and explain the analysis method.
That's actually much more useful.
My thoughts:
(1) M77 is not in a very nice place. It's near IceCube's edge. Not much can be done about that, short of dragging kilometers of ice to the equator. (Centaurus A might have been an even better candidate, but it is unfortunately even further south)
(2) I am not the biggest fan of the trend of ever more complicated statistics. 'We see a signal, but only with a boosted decision tree" is much less convincing than "we see a signal and it doesn't matter which statistical method we use" (got into an argument with an editor about that once). Some of this is taste, I admit, but a lot of it is it becomes very difficult to quantify significance. They say 4.2σ, but I do not believe that the probability that this is an artifact is 1/40,000. It is the probability of rejecting a very complex null hypothesis - no source and we perfectly understand the correlations in our MVA.
Do I think the signal is real? Yes, I do. I trust Francis (we can decide whether that is scientific or not), the result is plausible, and though the statistics are annoying, I doubt they are grossly wrong. I would say that "Evidence" is the right word for the title - that's what CDF used for evidence for the top quark at 2.8σ, and that turned out to be real. That had a p value of 1/400 and this feels about as certain, based on the technique.
It's not like the (now gone) Auger result which smelled fishy from the get go.