I suppose[ed] this was somewhat of a joke from the ISBA, prompted by Dennis Lindley, but as I [now] accord the actual extent of jokiness to be only ~10%, I’m sharing it on the blog [i]. Lindley (according to O’Hagan) wonders why scientists require so high a level of statistical significance before claiming to have evidence of a Higgs boson. It is asked: “Are the particle physics community completely wedded to frequentist analysis? If so, has anyone tried to explain what bad science that is?”
Bad science? I’d really like to understand what these representatives from the ISBA would recommend, if there is even a shred of seriousness here (or is Lindley just peeved that significance levels are getting so much press in connection with so important a discovery in particle physics?)
Well, read the letter and see what you think.
On Jul 10, 2012, at 9:46 PM, ISBA Webmaster wrote:
A question from Dennis Lindley prompts me to consult this list in search of answers.
We’ve heard a lot about the Higgs boson. The news reports say that the LHC needed convincing evidence before they would announce that a particle had been found that looks like (in the sense of having some of the right characteristics of) the elusive Higgs boson. Specifically, the news referred to a confidence interval with 5-sigma limits.
Now this appears to correspond to a frequentist significance test with an extreme significance level. Five standard deviations, assuming normality, means a p-value of around 0.0000005. A number of questions spring to mind.
1. Why such an extreme evidence requirement? We know from a Bayesian perspective that this only makes sense if (a) the existence of the Higgs boson (or some other particle sharing some of its properties) has extremely small prior probability and/or (b) the consequences of erroneously announcing its discovery are dire in the extreme. Neither seems to be the case, so why 5-sigma?
2. Rather than ad hoc justification of a p-value, it is of course better to do a proper Bayesian analysis. Are the particle physics community completely wedded to frequentist analysis? If so, has anyone tried to explain what bad science that is?
3. We know that given enough data it is nearly always possible for a significance test to reject the null hypothesis at arbitrarily low p-values, simply because the parameter will never be exactly equal to its null value. And apparently the LNC has accumulated a very large quantity of data. So could even this extreme p-value be illusory?
If anyone has any answers to these or related questions, I’d be interested to know and will be sure to pass them on to Dennis.
Professor A O’Hagan
Department of Probability and Statistics
University of Sheffield
So given that the Higgs boson does not have such an extremely small prior probability, a proper Bayesian analysis would have enabled evidence of the Higgs long before attaining such an “extreme evidence requirement”. Why has no one tried to explain to these scientists how with just a little Bayesian analysis, they might have been done
in last year or years ago? I take it the Bayesian would also enjoy the simplicity and freedom of not having to adjust to take account of what physicists call “the Look Elsewhere Effect” (LEE[ii]
Let’s see if there’s a serious follow-up.[iii]
[i] bringing it down from my “Msc Kvetching page” where I’d put it last night.
[ii] For a discussion of how the error statistical philosophy avoids the classic criticisms of significance tests, see Mayo & Spanos (2011) ERROR STATISTICS. Other articles may be found on the link to my publication page.
[iii] O’Hagan just informed me of several replies to his letter at the following:
According to Louis Lyons (“Discovery or fluke: Statistics in Particle Physics”, _Physics Today_ July 2012, pages 45-51):
“Current LHC analyses employ both [frequentist and Bayesian methods]. It is true that particle physicists tend to favor frequentist methods more than most other scientists do. But they often employ Bayesian methods for dealing with nuisance parameters associated with systematic uncertainties.”
… Not sure if it’s a coincidence or not, but this issue of _Physics Today_ also includes a commentary (by N. David Mermin) promoting a Bayesian interpretation of Quantum Mechanics, and also a book review of _The Theory That Would Not Die: How Bayes’ Rule …_.