Sorry for breaking this thread, sending along a couple of emails forwarded on with permission from another list where this was being discussed.
Email #1 below --srs(iPad) Begin forwarded message: > ----- Forwarded by Suresh Ramasubramanian1/India/IBM on 10/04/2011 07:47 AM > ----- > > From: "Joe St Sauver" <[email protected]> > To: Suresh Ramasubramanian1/India/IBM@IBMIN, > Date: 10/03/2011 06:53 PM > Subject: Re: Fw: [silk] UK judge bans Bayesian logic > > > > Hi Suresh, > > Thanks for passing along the pointer to the Guardian article > > # > http://www.guardian.co.uk/law/2011/oct/02/formula-justice-bayes-theorem-miscarriage > > The funny thing is that the bench in this case has actually weighed in, > perhaps unintentionally, on a long-standing debate in the statistical > community -- folks may or may not know this, but there are different > "camps" in the statistical community, much as there often is in many > different academic disciplines. > > For example, in the Decision Sciences Department at UO, the chair (and my > dissertation advisor) was an adherent of Fisher; another faculty member, > very well regarded, was a passionate and well published advocate of Bayes. > > If folks are curious what all the "fuss is about," I'd recommend the > article, "Why Isn't Everyone a Bayesian?" by B. Efron, from the February > 1986 American Statistician. A copy of that article is available online at > http://www.isye.gatech.edu/~brani/isyebayes/bank/EfronWhyEveryone.pdf > > If that article is too opaque, and you'd just like to see if you yourself > are a "latent Bayesian," consider the classic Monty Hall game show -- > for those of you who might never have seen it, Monty would select a member > of the audience and offer them the opportunity to pick one of three doors. > > Behind one door, there might be a terrific prize, such as a new car. > > Behind another door, there might be a gag prize such as a lifesize crude > ceramic billy goat, the perfect kitsch addition for your living room, eh? > > And then, behind the third door, there's some other prize, which might > be pretty cool, or pretty lame, it would vary, but usually be something > like a major appliance. > > Then again, sometimes Monty might have two lame prizes. > > The contestant gets to pick one door. At that point, what is his or her > chance of winning the high dollar value "good" prize, e.g., the car? > (most folks would say, 1-in-3) > > To make things more interesting, Monty would remind the contestant that > while there's a terrific prize behind one of the doors, they might not > have picked it. He'd then offer them cash-in-hand, if they want to > take the money and run. > > To "help" the contestant, Monty would also open one door. Since Monty knew > what door actually has the top prize, he'd never open that one. You > might see, instead, a nice washer and dryer set, or maybe the goat. > You'd never see the car (if there was a car). > > And now we come to the question that determines if you're a Fisherian > or a Bayesian at heart: > > *what's the probability that the contestant will win the car NOW that > Monty has opened one door?* > > Remember, there are two choices left, one of which has the car, one of > which does not. > > Fisher and his fans would say, obviously, 1-in-2, or 50%. > > Bayes and his adherents would say, no, the correct answer is 2-in-3, or > 66%. > > If you find yourself leaning toward Bayes, let me ask you an additional > question: assume the audience member is given the chance to *switch* > their choice, and pick the other unopened door. Should they? Would it > matter? If Fisher is right, both doors have an equal chance of being > right, and there's no reason why the person should switch. > > What would Bayesians say? :-; > > http://en.wikipedia.org/wiki/Monty_Hall_problem#Bayes.27_theorem > > Regards, > > Joe
