RIP Higgs Boson (with 95% confidence)

The LHC hasn't been running at 7GeV since March. AFAIK they have not fixed all the splices and are currently maxing out at around 3.5GeV

You can watch it live here (currently it is off):

http://op-webtools.web.cern.ch/op-webtools/vistar/vistars.ph...

    "we should discount our belief that the Higgs has a mass at 140GeV by a factor roughly proportionate to the 95% confidence of the result"

I'm sorry but I don't understand what this means in practice. The first part is a Bayesian belief, while the 95% confidence result comes from frequentist analysis. I'm not sure how you can mix the two.

Personally I don't have a very strong opinion on where the funding should go at all, just that it should exist and that it should be increased by an order of magnitude at least. Even experts in a field can have a hard time deciding where to allocate resources, what hope do I have? And more importantly what the hell business does Congress have providing for these allocations? They don't know shit.

I would rather shovel billions at universities with little more than an unenforced request that they spend it on pure research, than allow Congress any control over scientific funding at all.

Mainly I just think that drawing attention to scientific funding as some kind of waste of taxpayer money when it is such a drop in the bucket is more about serving the interests of the American conservative establishment in villainizing intellectuals than actually solving a problem.

It's a little more complicated, but "all" the energies ranges are searched in parallel.

It is easier to discard the ranges that are very far from the mass of the Higgs' boson. So initially the expected range is very broad, something like:

* More than 114GeV, because if it's smaller we would have seen the Higgs boson in another smaller accelerator (LEP)

* Less than 185GeV, because we saw small corrections that are probably due Higgs boson in the (LEP)

So you get a lot of money to build another accelerator, and you are confident that the maximal energy of the collider is enough to see something.

In some ranges, the experiments doesn’t show anything interesting, so it is possible to discard that the mass of the Higgs boson is in that range. It is easier to do this when the range is more far away from the "real" value. So you can discard with a 95% of confidence that range, get some papers published, perhaps a few Ph.D. thesis, compare the data to another more indirect calculations, show some progress, and ask for more money because the accelerator is really big.

The problem is that some energy ranges are more difficult to test, because other well known particles appear but the final results is very similar to what is expected from a Higgs boson. So it is important to choose some strange phenomenon where there is easier to see the difference between a Higgs boson and another particles. So with more experiments you can discard with a 95% of confidence a new range, ..., because the accelerator is really big.

But some ranges are more difficult to discard. There are a lot of interesting phenomenons. Some of them are due to other particles. The other particles are well known, so it is possible to calculate how many of these are expected to appear sadistically. But the experiments show that there are more than expected. It can be a statistical fluke, or it can be corrections that appear because the mass of the Higgs boson is near that range. The real problem is that if the Higgs boson really exists, a lot of corrections appear in the nearby mass ranges, so these ranges are more difficult to discard with a 95% confidence ...

The most difficult range is the one that includes the actual mass of the Higgs boson. It should be impossible to discard :). But it is not enough to not be able to discard it with a 95% confidence, because it can be a statistical fluke. To "prove" that the Higgs boson exists wits a 99.99997% confidence, more and more experiments are necessary to see the difference between a statistical fluke produced by the background process of the other particles and a real signal produced by the Higgs bosons. So you need more time to find it where it really is, than to discard it where it isn’t. (So you need more money to run the accelerator, so you need to dhow some preliminary results.)

So, next year we will probably see something like "RIP^2 Higgs Boson, 99% of the initial search range discarder forever with 95% confidence, only a minuscule 1% remaining." and it will be really a good new. And in a few (5?) years something like "Zombie Higgs Boson found, returned from 99.9% dead." and it will be a really good new.

The difference is that frequentist practice would be to stop at the 95% confidence interval and leave it there, whereas a Bayesian would use that observation to update their probability estimate of the theory being true.

"If the Higgs were at 140 GeV, it would have 5% probability of producing the results we measured experimentally" is the same as P(Observation | Higgs at 140Gev) = .05

So we can say that

  P(Higgs|Observation) = P(Observation|Higgs) * P(Higgs)
                         -------------------------------
                         P(Observation)

So given that getting your new belief about the probability of a Higgs Boson at some energy is going to be updated based on your observation, you can see that it ends up being scaled by that exact confidence result. That's sort of an oversimplification, since really you end up calculating the P(O) scaling factor based on P(O|H) among other things, but I hope you can see how they're closely related in practice.