

Discovery of the Higgs Boson rumoured to be at 3.5 sigma. - jsmcgd
http://www.math.columbia.edu/~woit/wordpress/?p=4212

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prawn
This is Hacker News - do we really need "god particle" added to the headline?
It's not present in the article.

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jsmcgd
Sorry prawn, on reflection I think you're probably right. It's unnecessary.

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windsurfer
I thought you were being rude but prawn really is his name.

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orijing
Well, if we take the 3.5 sigma at face value and bound it using Chebychev's
inequality [1], it seems that the discovery of the Higgs Boson is bounded by
1/3.5^2, which is 8%. In fact, the standard inequality is two-tailed. If we're
measuring just from one tail, we can use the single-sided inequality to yield
7.5%. Remember, we can't always assume a distribution is normal, a mistake
that even respected researchers often make.

[1] <http://en.wikipedia.org/wiki/Chebyshevs_inequality>

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sbayless
Hmm, I don't actually think chebyshev applies (in a meaningful way) in this
context. 3.5 sigmas refers to the probability of the observation being
significant, not the average mass of the higgs. Or did I misunderstand what
you meant?

As an aside, there is a typo in the parent's link:
<http://en.wikipedia.org/wiki/Chebyshev_inequality>

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tel
3.5 sigmas refers to the probability of some statistic being as severe as
they're observing under a model where the Higgs does not exist. Regardless of
the distribution, Chebyshev applies solely by assumption that sigma is a
meaningful unit. It may be overly conservative though.

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sarbogast
OK, now thanks to Wikipedia, I have a vague idea of what a higgs boson is and
why it is important. But could someone explain to me what those sigma's are
(in non Sheldon Cooper terms)? Is it a measure of the degree of certainty of
the particle actually being there?

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jerf
Yes. See <http://en.wikipedia.org/wiki/Standard_deviation> . In that first
graphical plot, the little σ after the number is lowercase Greek sigma. (The
upper case sigma, which may be more recognizable, is Σ, which you may
recognize as being used for summation.) Per the chart about halfway down the
page, a 5 sigma result means that there is a 1 / 1,744,278 probability that it
has come from pure chance.

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tomjen3
Buy that same table at 3 sigma there is still 99% chance that they have found
the damn thing.

Isn't it usually accepted that it is statistically significant when p goes
above 0.95? If so, why aren't they happy with a 20 times better result?

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jerf
Particle physicists generate data by the petabyte. If they used 3 sigma
confidence they'd confidently declare all sorts of false things. We know this,
because if you pay attention to particle physics you hear about all kinds of 3
sigmas that turn out to be spurious. (About every six months to a year or so,
I'd say.) 5 is just where they start to feel comfortable, they'll take more if
they can get it.

<http://www.nature.com/news/2011/110119/full/469282a.html>

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carbocation
Your answer is good and sufficient. For people who aren't yet getting an
intuitive feel: if 99% confidence means you're right 99% of the time (it
doesn't quite mean that but lets go with it), then you'll still be wrong 1% of
the time. If 3000 studies are published each year with that cutoff for
significance, you should expect about 30 spurious results accepted as true
each year. Ouch.

~~~
Estragon
That reasoning neglects the bias towards papers with interesting results,
which leads to a much higher rate of false reports in hot journals.

~~~
carbocation
In human genetics, studies will meta-analyze each of the ~million SNPs tested
across each study, rather than just picking the "candidate" SNPs that came to
attention because of their association signal in any particular study. So the
file drawer problem is still relevant, but the risk is greatly mitigated.

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orijing
I wonder if they can combine the experimental results from the 2.5 sigma and
the 3.5 sigma experiments. If two independent experiments confirmed some
hypothesis at 2.5 and 3.5 sigma, the combined evidence is surely much larger
than 3.5. Does anyone know what the right way of combining experimental
results is, to yield a more accurate answer?

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elwin
Assuming the errors are random and uncorrelated, the total significance is the
square root of the sum of the squares. In this case, that's only 4.3 sigma.

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nknight
> _only 4.3 sigma_

I generally treat particle physics as a black box from which magic appears,
but my understanding was that 3 is where things start getting interesting, and
5 is where it's considered pretty conclusive, so wouldn't going from 3.5 to
4.3 be a significant jump?

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akg
I was always curious how they measured these things. Does anyone have a good
reference that doesn't involve years of particle physics study?

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bmuon
It's a long way down the rabbit hole. There's a series of steps for measuring
in a particle accelerator and each itself is a big area of knowledge: \-
Detectors \- Hardware triggers \- Software triggers \- Data storage \-
Statistical analysis

I guess Wikipedia can give you an idea:
<http://en.wikipedia.org/wiki/ATLAS_experiment> A common statistical method
used in particle physics is the Monte Carlo method:
<http://en.wikipedia.org/wiki/Monte_Carlo_method>

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DaniFong
Sure, it's 3.5 sigma in this particular energy band, but is it 3.5 sigma in
every energy band?

It might be like expressing amazement that someone in the world won the
lottery. There's a difference between someone in particular winning the
lottery, and anyone winning the lottery.

Xkcd says it better than me. (hat tip to starwed)

<http://xkcd.com/882/>

~~~
bdonlan
They don't expect it to show up in every energy band - the whole point is that
they expect to see a lot of Higgs boson formation at a specific energy level,
and anything higher or lower drops to a background level. The sigma value is
basically a measure of how many standard deviations off from the background
event count the event count for this particular energy level is.

~~~
DaniFong
I'm sorry but I don't see how this addresses my point? If they are checking 20
bands for results with p < 0.05, the likelihood is that one will show up, just
from fluctuations from background.

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v21
Yes, but there's a prior prediction from theory that the Higgs will be within
this energy band.

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DaniFong
This specific one? What about all the other predictions over the years?

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eberfreitas
Honest question: what are they gonna do once they find it?

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jerf
First, a big celebration.

Then after the party, everybody has the hangover that may never end, because
finding the Higgs right where we expected it is potentially the worst case
scenario: <http://www.sciencemag.org/content/315/5819/1657.full>

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umarmung
Informative, but strange circular arguments in that article, especially from a
scientific process perspective.

There are a ton of questions that Higgs cannot answer already and yet if we
find Higgs precisely, research comes to a stop?

It almost feels like there's a split between theoretical physcists and
everyone else, with theoreticians saying if you take away our broken toy, you
better replace it with something we can play with!

Given Nature already trumped Einstein, his contemporaries, and all since, I
think we can be fairly secure that we will ALWAYS having find something new to
learn or discover from practical science.

After all, that's how we used to almost exclusively learn before scientists
went a bit crazy with maths. These days there seem to be many more models out
there than there is good science behind it - at least to a layperson like me.
:)

~~~
jerf
The meta-point is more that we need to find a deviation from the current
Standard Model. Further confirmations of the Standard Model are in a sense bad
news; we _want_ it to come apart so we can examine the pieces. It is true that
if we can produce the Higgs we can then study it, but if it then turns out to
precisely fit the parameters predicted by the SM, that's bad.

This argument should also be read along with the fact that last I knew, none
of the accelerators have been able to turn up anything else particularly
interesting either. Some of the supersymmetry theories predicted particles in
ranges that we should be able to see (barely) and none of them have appeared.
We're down to hoping that there's something else to find in the extra room the
LHC will give us at full blast or we really will be up a creek.

"These days there seem to be many more models out there than there is good
science behind it - at least to a layperson like me."

And in fact your observation is connected; particle physics has been starved
for data and in the interim have come up with all kinds of things, trying to
find things that may have testable consequences. This would go a lot better
with some data.

~~~
bdonlan
Surely there's still gravity left to explain away at the quantum level?

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btilly
There are irreconcilable differences between general relativity and quantum
mechanics. A lot of thought has gone into the problem, with little success.
But even if someone did come up with something concrete, what then? Try to
come up with an interesting experiment that combines gravity and quantum
mechanics.

I know of only one, and whether it tests anything at all depends on which
interpretation of QM you have. Based on a Geiger counter, either place, or
don't place a heavy weight. Try to measure its gravitational pull regardless
of what you do. It only measures a pull if you placed the object. If you
believe in the Everett interpretation, this says that gravity, at least to a
first order approximation, splits with the universe. We do not have sensitive
enough instruments to measure non-linear differences from GR.

History tells us that theoretical science done in the absence of experiment is
unlikely to lead to useful knowledge.

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martinkallstrom
What is this experiment called? Any links to read up on?

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atakan_gurkan
perhaps reading this <http://www.hedweb.com/everett/everett.htm>

(especially question 7) will help, even though it does not give the name for
such an experiment.

