I admit I'm not familiar with the model used to aggregate the boson data. But there's an entire community of nonparametric/semiparametric statisticians that works on problems just like this. It seems crazy to me that that millions of dollars are spent to build the machines to collect this data, yet the papers are written using statistical models with distributional/independence assumptions known to be false. (The tweet linked above seems to be saying something similar.)

Is there a concrete reason we can't be naive and just bootstrap confidence intervals for example? Of course I defer to the physicists here – but I'm curious whether there's some simple high-level reason the usual tricks don't work.