Some philosophy for ya

Jason Anastasopoulos writes,

I thought your blog readers might be interested in a philosophy professor at NYU whose work I discovered a few weeks ago. He’s one of the few that writes about the philosophy of probability and specifically on Bayesian theory. Here’s a link to his research page at NYU.

This looks interesting. I have a few points of disagreement or at least comment; maybe when I have time in March, I’ll write more on this. Until then, if you read the above papers and have questions about the foundations of probability, I’d suggest taking a look at chapter 1 of Bayesian Data Analysis, where we consider these issues from our own perspective, using examples from record linkage and football betting.

P.S. Jason adds:

There’s some really fascinating work going on in philosophy and history of science in probability as well . If you haven’t already, you should check out Ian Hacking, a philosopher of science that has written extensively on probability theory. I would recommend “The Taming of Chance” and
The Emergence of Probability: A Philosophical Study of Early Ideas about Probability, Induction and Statistical Inference.

7 thoughts on “Some philosophy for ya

  1. Hm, small world. Michael was at my house the other week. If you want to read another philosopher of probability (and who wouldn't want to hedge their bets with more than one?), there's Al Hájek out in Canberra, too.

  2. Sure, a bit more "philosophy" about causality and more generally probabilities is direly needed, because it seems (to me) that the basic question of choosing/defining the sample space is quickly swept under the rug in favor of "delightful" technical nitpickings over this or that method/algorithm or inane metaphysical hagglings (frequentists/bayesians).

  3. I've long been skeptical of some philosophy of science arguments. I think that some philosophers of science do not really understand the basic Bayesian method.

    Clark Glymour gives the following argument, in his essay "Why I Am Not A Bayesian."

    He claims that Bayesians cannot learn from old data.

    His argument goes thus: If E is old data, then P(E)=1; therefore (by an obvious theorem) P(E|T)=1 for theory T. Therefore,

    P(T|E)=P(E|T)*P(T)/P(E)=P(T)

    Since P(T|E)=P(T) the (alleged) Bayesian hasn't learned anything.

    The flaw in this argument is obvious, and the argument was effectively rebutted by Roger Rosencrantz in his essay, "Why Glymour Is A Bayesian." I have shown Glymour's argument to many working statisticans, who have invariably identified the obvious flaw. Distressingly, I have shown it to some philosophers of science, who have, even after the flaw is pointed out, have defended Glymour's argument.

    What is going on here?

  4. It IS a small world. I've just found this blog via Aaron Swartz's blog, where I was reading an interesting article about Wikipedia. Anyway, I'm a philosopher of statistics in Canberra, where I'm a colleague of Al Hájek (mentioned above) and a fan of John Carlin and therefore of your book Bayesian Data Analysis.

    As for Glymour's argument, well, it's hard to know what to say except that that paper of Glymour's is full of misunderstandings of what Bayesians actually do. Very few philosophers know what statisticians do … Glymour has less excuse than most, since he's in Teddy Seidenfeld's department, but generally people in field A don't know what people in field B do. Maybe it's as much the fault of the editors of the journals as the authors. Either way, it's sad. Anyway, thanks very much for the pointer to Rosencrantz's essay, which I didn't know about.

    Jason Grossman

  5. Jean Luc,

    I'm surprised by the lack of response to Glymour's posting. He has asked a fair question. I, too, would like to know what the obvious flaw is. (It's not obvious to me.)

    Alan

  6. I've heard a couple of comments on my comments above along the lines of "you claim that Glymour doesn't know anything about what statisticians do", so I thought I should clarify. This is a bit wordy, but hey, since I'm clarifying I'd better try to be precise.

    It seems to me that THAT PAPER of Glymour's ("Why I Am Not A Bayesian") is full of misunderstandings of what BAYESIANS do … specifically, Bayesian statisticians (and possibly also Bayesian philosophers, but I'm agnostic about what they do). That paper should be compared to the much earlier work (well known among Bayesians) by e.g. Lindley and Good (not to mention the positively prehistoric Harold Jeffreys, again well known to Bayesians), all of which tackle the problems Glymour mentions in that paper and (it seems to me) solve them. So my claim is that the paper should, at least, have referred to this previous literature.

    Note the two narrowings of scope there: I'm referring one very old paper of Glymour's, and I'm referring to its understanding of previous work in the Bayesian tradition. So it's not a comment on Glymour's (in general) undestanding of statistics (in general).

    Since that paper was a very influential one, I may write more about this some time … but whether I do or not, these should not be taken as comments on the CURRENT debate.

Comments are closed.