Thanks for a most interesting topic, which led to a great discussion over dinner. The scientific model my husband uses in his research is Bayesian, and so I HAD to know how the past could not be determined, since it has already happened.
I got a neat talk on data-poor vs. data-rich fields. On Aug 7, 2011, at 6:56 PM, ERIC P. CHARLES wrote: > Russ, > Very nice calculations. It would have taken me quite a while to figure it > out. Thanks! > > Tom, > Interesting article. At the end though, I think the review's author misses > the point of why Bayes theorem was so controversial amongst the 'frequents' > (which suggests the book's author might have missed the point as well). The > controversy occurred because many early statisticians wanted to believe in a > truly probabilistic future, but believed in an already determined past -- > basically what most people believe in. In that sense, there is a probability > that you will pick the counterfeit coin before you make the choice, the 'a > priori' probability (given a random choice) is .33. After you pick a coin, > either you picked the conterfeit one or you did not, thus there is no > probability worth discussing; the 'a posteriori' probability that you picked > the counterfeit coin is either 1 or 0. Once the coin is in my hand, and no > matter how many times I flip it, there will never be a 4/5ths chance that I > picked the counterfeit coin. What would that even mean?!? Or so the > anti-Bayes people argued: We can talk about our best guess as to the truth > all day, but we are NOT talking about probability when we do so. > > Fisher tried to deal with the problem of using the present to guess the past > with his 'likelihood' formulae. Under some circumstances likelihood and Bayes > theorem will come to the same number, but other times they will not. > Likelihood calculations are still around, but not as popular as Bayes, > because it is much harder to derive the formulae (and sometimes harder to > gather the needed data). Fun fact: Researcher's reliance on Bayes formula was > what lead Fisher to insist throughout his life that there was no evidence > that smoking caused cancer. There is now evidence he would accept, but no > data at the time allowed what he deemed to be the proper calculations. > > Eric > > P.S. For any stats people who might be reading, I have published on the > problem of creating confidence intervals around correlations corrected for > attenuation due to measurement error. If your population correlation is near > 0, then the probability distribution for sample correlations is symmetric, > and likelihood and Bayes will give you the same answer. As you approach 1 (or > -1), the probability distributions becomes highly asymmetric, and likelihood > and Bayes will give quite different answers. (Confession of mathematical > inadequacies: I tackled the problem through simulation, not through > derivation). > > > > On Sun, Aug 7, 2011 07:48 PM, Russ Abbott <[email protected]> wrote: > When I read that review it wasn't obvious to me how he got the result that he > did for the counterfeit coin example. So I worked it out for myself--and > after a bit of thinking about it got the same answer. If you're interested > it's here. (Let me know if you think I made any mistakes.) The calculation is > at the bottom of the Bayes Theorem page on my wiki. > > -- Russ Abbott > _____________________________________________ > Professor, Computer Science > California State University, Los Angeles > > Google voice: 747-999-5105 > blog: http://russabbott.blogspot.com/ > vita: http://sites.google.com/site/russabbott/ > _____________________________________________ > > > > On Sun, Aug 7, 2011 at 2:41 PM, Tom Johnson <[email protected]> wrote: > A review of a new book that may be of interest. > --tom johnson > > The Mathematics of Changing Your Mind > By JOHN ALLEN PAULOS > Published: August 5, 2011 > > Sharon Bertsch McGrayne introduces Bayes’s theorem in her new book with a > remark by John Maynard Keynes: “When the facts change, I change my opinion. > What do you do, sir?” > > Bayes’s theorem, named after the 18th-century Presbyterian minister Thomas > Bayes, addresses this selfsame essential task: How should we modify our > beliefs in the light of additional information? Do we cling to old > assumptions long after they’ve become untenable, or abandon them too readily > at the first whisper of doubt? Bayesian reasoning promises to bring our views > gradually into line with reality and so has become an invaluable tool for > scientists of all sorts and, indeed, for anyone who wants, putting it > grandiloquently, to sync up with the universe. If you are not thinking like a > Bayesian, perhaps you should be. > > http://www.nytimes.com/2011/08/07/books/review/the-theory-that-would-not-die-by-sharon-bertsch-mcgrayne-book-review.html?_r=1&ref=books > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org > Eric Charles > > Professional Student and > Assistant Professor of Psychology > Penn State University > Altoona, PA 16601 > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org "In humans, the brain is already the hungriest part of our body: at 2 percent of our body weight, this greedy tapeworm of an organ wolfs down 20 percent of the calories that we expend at rest." Douglas Fox, Scientific American
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