## sunrise

Posted in pictures, Statistics, Travel, University life with tags , , , , , on November 30, 2011 by xi'an

## is the p-value a good measure of evidence?

Posted in Statistics, University life with tags , , , , , , , on November 30, 2011 by xi'an

Statistics abounds criteria for assessing quality of estimators, tests, forecasting rules, classification algorithms, but besides the likelihood principle discussions, it seems to be almost silent on what criteria should a good measure of evidence satisfy.” M. Grendár

A short note (4 pages) appeared on arXiv a few days ago, entitled “is the p-value a good measure of evidence? an asymptotic consistency criterion” by M. Grendár. It is rather puzzling in that it defines the consistency of an evidence measure ε(H1,H2,Xn) (for the hypothesis H1 relative to the alternative H2) by

$\lim_{n\rightarrow\infty} P(H_1|\epsilon(\neg H_1,H_2,X^n)\in S) =0$

where S is “the category of the most extreme values of the evidence measure (…) that corresponds to the strongest evidence” (p.2) and which is interpreted as “the probability [of the first hypothesis H1], given that the measure of evidence strongly testifies against H1, relative to H2 should go to zero” (p.2). So this definition requires a probability measure on the parameter  spaces or at least on the set of model indices, but it is not explicitly stated in the paper. The proofs that the p-value is inconsistent and that the likelihood ratio is consistent do involve model/hypothesis prior probabilities and weights, p(.) and w. However, the last section on the consistency of the Bayes factor states “it is open to debate whether a measure of evidence can depend on a prior information” (p.3) and it uses another notation, q(.), for the prior distribution…  Furthermore, it reproduces the argument found in Templeton that larger evidence should be attributed to larger hypotheses. And it misses our 1992 analysis of p-values from a decision-theoretic perspective, where we show they are inadmissible for two-sided tests, answering the question asked in the quote above.

## most hated airport in the World!

Posted in pictures, Travel with tags , , , on November 29, 2011 by xi'an

The Charles de Gaulle airport, on which I posted my list of complaints a while ago, has been nominated “the most hated airport in the world” by CNN Go. They mentioned

“Grimy washrooms with missing toilet seats don’t help. Nor do broken scanning machines and an overall lack of signage, gate information screens and Paris-worthy bars, restaurants or cafés. The baffling circular layout is worsened by warrens of tunnel-like structures, dismissive staff and seething travelers waiting forever in the wrong queue.”

This is about Terminal 1, whose circular design is indeed nonsensical since there are only two exits to the circle. The picture on the site is in Terminal 2, with the huge posterboard at the exit of the train station. My complaint with Terminal 2 (I rarely use Terminal 1 for frequent-flyer reasons) is not about the toilets (they are fine by French standards), nor about scanning machines (I actually registered for an automated passport scan that cuts queues dramatically when both entering and leaving the country), nor about the bars and restaurants (I do not eat, nor drink), but rather about the poor design (or rather the outgrowth of the design:) a linear layout of the airport that forces travellers to walk long distances (often doubled by the fact that the luggage room exit is as far as possible from the train station) since there is no inner train, a flight density that often induces bussing passengers for dozens of minutes (this is always the case when flying to the UK), and a very poor train connection to down town Paris (there is no direct train, all trains stop in a myriad of Northern suburban cities).

## Error and Inference [arXived]

Posted in Books, Statistics, University life with tags , , , , , , , on November 29, 2011 by xi'an

Following my never-ending series of posts on the book Error and Inference, (edited) by Deborah Mayo and Ari Spanos (and kindly sent to me by Deborah), I decided to edit those posts into a (slightly) more coherent document, now posted on arXiv. And to submit it as a book review to Siam Review, even though I had not high expectations it fits the purpose of the journal: the review was rejected between the submission to arXiv and the publication of this post!

## R exam

Posted in Kids, pictures, Statistics, University life with tags , , , , , , , on November 28, 2011 by xi'an

Following a long tradition (!) of changing the modus vivendi of each exam in our exploratory statistics with R class, we decided this year to give the students a large collection of exercises prior to the exam and to pick five among them to the exam, the students having to solve two and only two of them. (The exercises are available in French on my webpage.) This worked beyond our expectations in that the overwhelming majority of students went over all the exercises and did really (too) well at the exam! Next year, we will hopefully increase the collection of exercises and also prohibit written notes during the exam (to avoid a possible division of labour among the students).

Incidentally, we found a few (true) gems in the solutions, incl. an harmonic mean resolution of the approximation of the integral

$\int_2^\infty x^4 e^{-x}\,\text{d}x=\Gamma(5,2)$

since some students generated from the distribution with density f proportional to the integrand over [2,∞) [a truncated gamma] and then took the estimator

$\dfrac{1-e^{-2}}{\frac{1}{n}\,\sum_{i=1}^n y_i^{-4}}\approx\dfrac{\int_2^\infty e^{-x}\,\text{d}x}{\mathbb{E}[X^{-4}]}\quad\text{when}\quad X\sim f$

although we expected them to simulate directly from the exponential and average the sample to the fourth power… In this specific situation, the (dreaded) harmonic mean estimator has a finite variance! To wit;

> y=rgamma(shape=5,n=10^5)
> pgamma(2,5,low=FALSE)*gamma(5)
[1] 22.73633
> integrate(f=function(x){x^4*exp(-x)},2,Inf)
22.73633 with absolute error < 0.0017
> pgamma(2,1,low=FALSE)/mean(y[y>2]^{-4})
[1] 22.92461
> z=rgamma(shape=1,n=10^5)
> mean((z>2)*z^4)
[1] 23.92876


So the harmonic means does better than the regular Monte Carlo estimate in this case!

## art brut

Posted in pictures with tags , , on November 27, 2011 by xi'an

## black man [a.k.a. TH1RTE3N]

Posted in Books with tags , , , , , , , , on November 27, 2011 by xi'an

Human intuition is deceptive because it is not always consistent. It is not necessarily a good fit for the environments we now live in, or the mathematics that underlie them. When it does echo mathematical form, it’s clearly indicative of an inherent capacity to detect that underlying mathematics (…) When they clash, the mathematics remains correct. The intuition merely indicates a mismatch of evolved capacities with a changed or changing environment.Black Man, p.441

thirteen is the only genetic variant Jacobsen thought dangerous enough to abrogate basic human rights on. You’re talking about a type of human this planet hasn’t seen in better than twenty thousand years.Black Man, p.102

This is the last book by Richard K. Morgan I read (after the Kovacs series, Market Forces, and The Steel Remains). It has also  been published under the title Thirteen (or Th1rte3n..) Black Man has some resonance with Broken Angels, with the central hero, Carl Marsalis, having some common points with Takeshi Kovacs. However, while the theme of a future hard-boiled hired detective in a bleak future is found in both novels, both Carl Marsalis and the tone of the novel are much more pessimistic than the Kovacs series, with no-one getting a clean and nice grade by the end of the book… The description of the future Earth is less technical than in the other novels, the focus being more on race, power, and politics. Carl Marsalis himself is facing a double stigma in this futuristic society, by being a black man and a genetically modified human, restored to the primal urges of 20,000 BC Homo Sapiens, a “thirteen”. Add to this being a traitor to his group by hunting runaway thirteens for a UN police force.

Carl entered the equation with no local axe to grind, and nothing to loose…Black Man,  p.305

The book starts like a space opera, but quickly gets grounded to the former U.S.A., split between a relatively tolerant Rim and backward Jesusland. The action immediately quicks in as well with many characters central to one chapter and dispatched in the next. Which made my reading the first hundred pages a bit hard. But after that the central characters were well-enough done to get familiar and the remainder of the story went by very very fast…

After a while, when you’re on your own out there, you start making patterns that aren’t there. You start asking yourself, why you? Why this fucking statistical impossibility of a malfunction on your watch? You start to think there’s some kind of malignant force out there.Black Man, p.328

Judging from some reviews found on the web, readers seem to prefer the Kovacs series. I am more ambivalent, in the sense that the pace and setup of the series is more grandiose and breath-taking. However, the less military/more political [in the wide sense] vision of the Black Man really got me in its grip and the ending(s) was (were) a superb piece of literature. The  announced departure of one of the major characters is very well rendered. Both novels are excellent books, that’s all! To wit, one got the Philip K. Dick Award, while the other got the Clarke Award. (Somehow inverted: Black Man would have been more fitting for the Philip K. Dick Award. If only because Marsalis’ hunt for fellow thirteens was reminded me of Deckhard’s parallel hunt in Blade Runner—a.k.a. Do Androids Dream of Electric Sheep?)