Tag Archives: Statistics

Innumeracy

From testimony by Michael Gove, British Secretary of State for Education, before their Education Committee:

Q98 Chair: One is: if “good” requires pupil performance to exceed the national average, and if all schools must be good, how is this mathematically possible?

Michael Gove: By getting better all the time.

Q99 Chair: So it is possible, is it?

Michael Gove: It is possible to get better all the time.

Q100 Chair: Were you better at literacy than numeracy, Secretary of State?

Michael Gove: I cannot remember.

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Survivorship Bias

See also this excellent paper

 

You Are Not So Smart

The Misconception: You should focus on the successful if you wish to become successful.

The Truth: When failure becomes invisible, the difference between failure and success may also become invisible.

In New York City, in an apartment a dozen blocks west of Harlem, above trees reaching out over sidewalks and dogs pulling at leashes and conversations cut short to avoid parking tickets, a group of professional thinkers once gathered and completed equations that would both snuff and spare several hundred thousand human lives.

People walking by the apartment at the time had no idea that four stories above them some of the most important work in applied mathematics was tilting the scales of a global conflict as secret agents of the United States armed forces, arithmetical soldiers, engaged in statistical combat. Nor could people today know as they open umbrellas and twist heels on cigarettes, that nearby, in an apartment overlooking Morningside…

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The Exchange Paradox

Photograph by Jake Slagle @ flickr

 

“A swami puts m dollars in one envelope and 2m dollars in another. You and your opponent each get one of the envelopes (at random). You open your envelope and find x dollars, and then the swami asks you if you want to trade envelopes. You reason that if you switch, you will get either x/2 or 2x dollars, each with probability 1/2. This makes the expected value of a switch equal to (1/2)(x/2) + (1/2)(2x)=5x/4, which is greater than the x dollars that you hold in your hand. So you offer to trade.

 

The paradox is that your opponent has done the same calculation. How can the trade be advantageous for both of you?”

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Larry Laudan. Why Presuming Innocence is Not a Bayesian Prior

“…the presumption (of innocence) is not (or at least should not be) an instruction about whether jurors believe defendant did or did not commit the crime. It is, rather, an instruction about their probative attitudes.”

Error Statistics Philosophy

DSCF3726“Why presuming innocence has nothing to do with assigning low prior probabilities to the proposition that defendant didn’t commit the crime”

by Professor Larry Laudan
Philosopher of Science*

Several of the comments to the July 17 post about the presumption of innocence suppose that jurors are asked to believe, at the outset of a trial, that the defendant did not commit the crime and that they can legitimately convict him if and only if they are eventually persuaded that it is highly likely (pursuant to the prevailing standard of proof) that he did in fact commit it. Failing that, they must find him not guilty. Many contributors here are conjecturing how confident jurors should be at the outset about defendant’s material innocence.

That is a natural enough Bayesian way of formulating the issue but I think it drastically misstates what the presumption of innocence amounts to.  In my view, the…

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R.I.P. George E.P. Box

box

Last Thurs­day (28 March 2013), George Box passed away at the age of 93. He was one of the great sta­tis­ti­cians of the last 100 years, and leaves an aston­ish­ingly diverse legacy.

When I teach fore­cast­ing to my sec­ond year com­merce stu­dents, we cover Box-​​Cox trans­for­ma­tions, Box-​​Pierce and Ljung-​​Box tests, and Box-​​Jenkins mod­el­ling, and my stu­dents won­der if it is the same Box in all cases. It is. And we don’t even go near his work on response sur­face mod­el­ling, design of exper­i­ments, qual­ity con­trol or ran­dom num­ber gen­er­a­tion. Occa­sion­ally, a stu­dent won­ders if box­plots are also due to GEP Box, but they were the brain­child of his good friend John W Tukey.

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I would definitely add to the list the following paper which Rob Tibshirani was too modest to include:
R Tibshirani (1996) – Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society. Series B (Methodological), 267-288

Normal Deviate

GUEST POST: ROB TIBSHIRANI

Today we have a guest post by my good friend Rob Tibshirani. Rob has a list of nine great statistics papers. (He is too modest to include his own papers.) Have a look and let us know what papers you would add to the list. And what machine learning papers would you add? Enjoy.

9 Great Statistics papers published after 1970
Rob Tibshirani

I was thinking about influential and awe-inspiring papers in Statistics and thought it would be fun to make a list. This list will show my bias in favor of practical work, and by its omissions, my ignorance of many important subfields of Statistics. I hope that others will express their own opinions.

  1. Regression models and life tables (with discussion) (Cox 1972). A beautiful and elegant solution to an extremely important practical problem. Has had an enormous impact in medical science. David Cox…

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