Comments on: Thanksgiving

By: Everybody Get Ya Bos-on | Sciencey Things

Everybody Get Ya Bos-on | Sciencey Things — Fri, 16 Dec 2011 09:53:37 +0000

[...] “I heard a lot about statistics and sigmas. WTF?” Sean Carroll with an explanation of “confidence” sigmas. [...]

By: “The fault, dear Brutus, is not in our detectors, but in ourselves.” « Galileo's Pendulum

Tue, 13 Dec 2011 16:04:00 +0000

[...] a particle where there is none. That’s tough, but that’s particle physics for you. Only a result of 5 sigma (which again should appear in 2012 if all goes well) is good enough for scientists to say [...]

By: The Higgs Confidence Game « Gödel’s Lost Letter and P=NP

The Higgs Confidence Game « Gödel’s Lost Letter and P=NP — Tue, 13 Dec 2011 08:37:10 +0000

[...] A first-time or one-off or rare event, however, heightens the inconvenient question discussed here by physicist and blogger Sean Carroll: What are the error bars on your error [...]

By: Thanksgiving | Cosmic Variance | Discover Magazine | Secularity (under construction)

Thu, 01 Dec 2011 23:36:08 +0000

[...] Thanksgiving | Cosmic Variance | Discover Magazine. Share this:TwitterFacebookLike this:LikeBe the first to like this post. By Colin Mackay 0 [...]

By: Phillip Helbig

Phillip Helbig — Mon, 28 Nov 2011 15:29:21 +0000

Indeed. One needs the likelihood as a function of the parameters. These days, there is no excuse for not sticking it on the web: http://www.astro.multivax.de:8000/ceres/data_from_papers/papers.html .

For contours, I plot the smallest contour which encloses, say, 95% of the integrated likelihood, not some percentage of the peak likelihood (I’ve seen this done, with the percentage chosen so that it corresponds to 95% c.l. for a gaussian distribution, even if the data are not gaussian.)

By: Mr D

Mr D — Sun, 27 Nov 2011 02:40:32 +0000

I’ll have to disagree.

In X-ray astronomy, I’d go so far as to characterize error bars and simple uncertainties as being a big problem. The underlying distributions are often very covariant or even completely non-Gaussian, but most authors will simply quote symmetrical uncertainties and be done with it, as if that made any sense. Some will be fancy and include asymmetrical uncertainties, as if that made it any better… And the reviewers are apparently fine with this.

I’m done with simple uncertainties, it’s marginalized likelihood contours that we should be publishing, with the underlying MCMC data available somewhere for use in future studies.

By: David Brown

David Brown — Sat, 26 Nov 2011 11:42:23 +0000

A group of scientists sitting at a Thanksgiving feast table and saying aloud, “Let us give thanks to whatever there is for error bars, Hubble’s Law, and the Spin Statistics Theorem” might be a plausible cartoon for Gary Larson’s “Far Side”.

By: Massimo

Massimo — Fri, 25 Nov 2011 20:00:39 +0000

If the underlying distribution has a finite variance, right ?

This is one of the conditions upon which the central limit theorem, in the form that most of us have learned, indeed applies. At the time I was told by the person teaching it, that it is possible to relax the conditions, but the proof becomes rather unwieldy.
Interestingly, one can come to the conclusion that the underlying distribution function is a Gaussian, assuming that mean value and standard deviation are known, without invoking the central limit theorem at all. If one simply adopts a Bayesian viewpoint, the Gaussian is the distribution that maximizes the entropy — see, for instance, D. Sivia, “Data Analysis: A Bayesian Tutorial”.

By: JW Mason

JW Mason — Fri, 25 Nov 2011 18:45:31 +0000

An error bar is basically the standard deviation

I’m curious about the “basically” here. In what sense is the error bar not the (estimated) standard deviation?

a histogram of the sums of random numbers approaches the normal distribution as the number of random numbers per sum approaches infinity. For processes in which the total error is the sum of many uncorrelated errors, this is applicable.

If the underlying distribution has a finite variance, right? Which is not the case for all natural processes.

In the social sciences, the assumption of uncorrelated errors is also a major problem. For you guys in the physical sciences, I guess not so much.

By: Phillip Helbig

Phillip Helbig — Fri, 25 Nov 2011 11:16:51 +0000

What is not obvious to many is the reason why the normal distribution is such a common error distribution. Answer: a histogram of the sums of random numbers approaches the normal distribution as the number of random numbers per sum approaches infinity. For processes in which the total error is the sum of many uncorrelated errors, this is applicable.

By: Georg

Georg — Fri, 25 Nov 2011 11:16:31 +0000

Hell what science history falsification!
Gauß did not “make it popular” he invented it,
and he did that on purpose.
So it is not “”The nice thing about a normal distribution is that it is fully specified by just two numbers “” but it is a property he looked for when
he was told to supervise the triangulation results of the Hannoverian country.
So, the thanks could be directed to Gauß for not just demanding
one or another length or angle measured once more, he thought
on the problen basically and as ingenious as usual.
Or thank someone in the Hannoverian ministy to gave him the order mentioned
or thank the one who looked for that young Gauß was sent to schools
when he showed signs of some math genious as a boy.

By: Thomas

Thomas — Fri, 25 Nov 2011 10:41:37 +0000

Dammit Sean, I was about to lazily just plot my means without error bars, now I feel obliged to comply.

By: Chris

Chris — Fri, 25 Nov 2011 04:06:25 +0000

While we scientists are thankful for the error bar and love everything it tells us, the students we teach despise it and believe it was created just to torment them.

Although I am tempted to put the standard model Lagrangian on their final general physics equation sheet. We have to torment them a little

By: Mike

Mike — Fri, 25 Nov 2011 02:28:24 +0000

I’m giving thanks for the Enlightenment. It’s only been several hundred hears, but the world has changed greatly for the better. Let’s all hope and work for it continuing. It’s the only h0pe we have — short of ET dropping in and making it all right.

By: Lab Lemming

Lab Lemming — Fri, 25 Nov 2011 00:39:29 +0000

“(Like maybe a Nobel-prize-worthy discovery?)”

Or, for those of us in the 99%, a stupid technical mistake…