Tag Archives: Bayes

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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Overdiagnosis and Overtreatment

Here is a nice article on overtreatment by Kevin McConway:

Screening for disease was in the news again in the UK last week. According to the BBC, a 20-year Swedish study of screening for prostate cancer showed that screening brought no benefit. (The actual study report didn’t put it quite so baldly, but effectively did conclude there was no benefit.) This came just a couple of days after the Alzheimer’s Disease Society asked that the NHS should offer checks for dementia to everyone (in the UK) when they reach the age of 75. Both these news items reported contrasting views on whether these screening checks are in fact advisable.

Why is that? You might think that it’s surely better to know whether someone has a disease than not to know, and if some sort of screening or check can give this information, well, why not just do it?

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