Archive for conditioning

Bayes is back on xkcd

Posted in Books, Kids, Statistics with tags , , , on July 12, 2013 by xi'an

Cross validated question

Posted in R, Statistics, University life with tags , , , on February 20, 2012 by xi'an

Another problem generated by X’validated (on which I spent much too much time!): given an unbiased coin that produced M heads in the first M tosses, what is the expected number of additional tosses needed to get N (N>M) consecutive heads?

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Monty Hall, again

Posted in Books, Statistics with tags , on February 24, 2010 by xi'an

This little article contains nothing new, and only almost trivial mathematics. It is a plea for future generations to preserve the life of The True Monty Hall paradox, and not let themselves be misled by probability purists who say “you must compute a conditional probability”.

Richard Gill posted a paper on arXiv this morning about the Monty Hall problem. He does not mean to try yet another solution to the problem more susceptible to convince the army of skeptics out there, but rather to illustrate the hidden and implicit assumptions behind the mathematisation (sic!) of the problem… As a background to the problem, Richard Gill refers to the book The Monty Hall Problem: The Remarkable Story of Math’s Most Contentious Brain Teaser that led to my earlier post. Now, after having read the paper and come upon the final sentence reported above, I must say I am none the wiser about why the author wrote the paper! To me the Monty Hall problem is primarily an instance of wrong conditioning… Nonetheless, I appreciate the points about visualising the puzzle as a decision theoretic problem and the solution as the minimax procedure.

The Monty Hall “problem”

Posted in Books, Statistics with tags , , , on February 4, 2010 by xi'an

I stumbled by chance on this book The Monty Hall Problem: The Remarkable Story of Math’s Most Contentious Brain Teaser on Amazon, or rather and more accurately Amazon suggested the book as connected to Burdzy’s The Search for Certainty. I first thought why would anyone need a whole book for explaining a simple conditioning argument (and the fallacy of conditioning on the wrong event) that I usually give as a problem to my second year undergraduates. But then I started reading the comments and found one that could not believe there was such a book because the answer was clearly 50-50! (Obviously, this comment was written by someone who had not read the book…) And I thus vaguely remembered a story about a highly respectable and respected statistician getting trapped by this puzzle… So maybe a book is in order. Maybe. But I find the argument of one of the commenters of the above disbelieving comment quite convincing: imagine there are 10,000 doors (instead of just 3), you pick one, the host opens 9,998 out of the 9,999 remaining ones and let you decide between switching  to the last remaining door and sticking to your original choice. Would you ever stick?!