Originally Posted by
DuB
At the risk of further increasing the pedantry level, I have some comments on the "certainty" issue.
I was confused by the 1/400 figure (what the hell does it mean to be "1/400 certain"?) so I poked around a bit to see where that figure comes from. Apparently theory holds that the presence of a Higgs should manifest itself as an excess of energy in the "gamma-gamma channel" (whatever that is), and the event that is causing all this fuss was the observation of an excess of energy in the expected channel of about 3 or 3.5 standard errors above what is normally expected in that channel. In other words, if you think about the range of energy levels that one would expect to observe in that channel--when nothing is actually going on!--as a normal distribution or "bell-shaped curve" of energy levels, then this excess was about 3 standard deviations (or sigma, which the authors of the article in the OP amusing spell "sygma") above the mean of that sampling distribution, which is starting to get pretty far out into the positive tail. The area under the curve (or probability density) of an event greater than 3 sigma or less than 3 sigma is about .00269, or about 1/369. As far as I can tell, this is where the 1/400 figure comes from.
Let's be careful about how we interpret this 1/369 figure. Assuming that what I wrote above is indeed where the figure comes from, then this figure is basically a "p-value," as cmind noted. That is, it is the probability of the observed data, conditional on the hypothesis being false. In other words, if it is in fact the case that there was no Higgs at all, then the odds of seeing an excess of energy of the magnitude that we did are about 369 to 1 against. What is very important to realize is what this figure is not. It is not--and this is important--the probability of the hypothesis being true (or false), conditional on the observed data (that is, the probability that we actually observed a Higgs). We would call such a probability a posterior probability. Arguably this probability is what we really want to know most. Unfortunately, in general P(D|H) does not equal P(H|D). Arriving at this latter probability requires additional information, namely, a distribution of prior probabilities. Although closer, it is also not a type 1 error rate (that is, the probability that we have incorrectly concluded that we observed a Higgs). Such a probability is called an alpha level, and is in fact specified a priori by the data analyst--we know that the probability of a type 1 error will be equal to the chosen alpha level before we ever collect any data.
None of this is to denigrate the present findings. But let's be clear about what exactly is meant when we talk about things like 1/400 certainty.
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