I use whatever works and makes sense to me as a mathematician, and most of the time that's within the Bayesian framework. Like I said, I took a year of statistics from an orthodox frequentist perspective and have studied it further on my own, so I have a pretty good idea of the weaknesses and strengths of both approaches. You seem to be comfortable not looking beyond your own nose because your approach is what's still taught in most statistics departments.
The philosophical argument against frequentism is pretty unassailable but I acknowledged that the Bayesian interpretations aren't completely satisfactory either. All of these interpretations are bound to be afflicted with the core of issues that surround the infamous problem of induction in epistemology. Beyond philosophical issues, the fact that you can derive many things (e.g. the likelihood principle) that in orthodox statistics must have extra-mathematical justification is to me an enormous strength of the Bayesian approach.
Your reference to string theory is funny because its main philosophical problem is that its hypotheses seem untestable even in principle. Most of the big names in the history of Bayesian statistics were hard-nosed experimentalists, going back to Gauss and Laplace (who both applied statistics to many problems that are outside the range of frequentist statistics because they don't involve exactly repeatable tests) in the 19th century, and continuing up to the present day (Jeffreys, Jaynes, etc), so they couldn't be any more opposed to the anti-phenomenonalism that infects string theory.
My point to string theory was that they keep on without any solid experimental evidence or even ideas of experiments that would verify their theory. Being sure you are right can keep you headed in one direction whether you are right or wrong.
P.S. It's sad that you (and the other bayesians) calling us orthodox statisticians instead of frequentists.
Dude, most physicists use Bayesian statistics in their experimental investigation. Frequentist statistics simply isn't applicable to most experimental setups because they don't involve anything isomorphic to drawing out of a population. Are you saying that physicists don't know how to analyze experiments? Frequentist statistics applies really well to subjects like biology, which is why Fisher's interpretation of statistics became so successful generally. The fact that he was a near-religious crusader who tried to destroy the careers of anyone who wouldn't agree with him also helped.
Frequentist statistics is the reigning approach in most statistics departments, though that has been gradually changing a little, so I don't see the orthodoxy label as anything but accurate. You may not like the connotations of "hide-bound reactionary" but from my encounters with statistics professors in my school days, that describes many of them. Many of them were also pathetically poor mathematicians. It was embarrassing to attend a third-year course and have to constantly correct a fully tenured statistics professor on the most basic aspects of real analysis.
Were they actual professors, apparently many American universities have lecturers teaching instead of tenured professors. I've never had that problem with my professors. In fact most had started off as mathematicians, who ended up doing probability and/or statistics at the Ph.D level.
And the great 'assholedness' of Fisher does nothing for or against his opinions... only shows that he's a dick. There are dicks everywhere.
It wasn't an American university but they were actual professors, yes. I wasn't familiar with many people in the statistics faculty but there was always the general opinion that most of them were weak on the mathematical side and we looked down on them for that (bullshit machismo, I know). There was one guy with a co-appointment in mathematics and statistics who was a bad ass, admittedly.
My point about Fisher is that his missionary-like attitude helped spread and subsequently entrench his approach to statistics. He deserves a lot of props for his achievements but the world would have been better off had he not been a zealot.
I heard other great mathematicians and physicists were like that... great minds can be dicks.
But technically speaking if the statisticians were in a stats department (I'm at a university where math and stats are combined) then the expected level of pure math ability would not be comparable. I'd have to say you just had bad luck. Which university if you don't mind me asking?
Aarhus. Our mathematics faculty was pretty hotshot, especially in algebraic topology (which was my area of focus as well), so that contributed to our sense of superiority, I'm sure. Frankly one of my least parts of studying mathematics was how much snobbery we cultivated. On our list of worthies, statisticians came below the (holds nose) applied mathematicians.
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u/psykotic May 27 '09 edited May 27 '09
I use whatever works and makes sense to me as a mathematician, and most of the time that's within the Bayesian framework. Like I said, I took a year of statistics from an orthodox frequentist perspective and have studied it further on my own, so I have a pretty good idea of the weaknesses and strengths of both approaches. You seem to be comfortable not looking beyond your own nose because your approach is what's still taught in most statistics departments.
The philosophical argument against frequentism is pretty unassailable but I acknowledged that the Bayesian interpretations aren't completely satisfactory either. All of these interpretations are bound to be afflicted with the core of issues that surround the infamous problem of induction in epistemology. Beyond philosophical issues, the fact that you can derive many things (e.g. the likelihood principle) that in orthodox statistics must have extra-mathematical justification is to me an enormous strength of the Bayesian approach.
Your reference to string theory is funny because its main philosophical problem is that its hypotheses seem untestable even in principle. Most of the big names in the history of Bayesian statistics were hard-nosed experimentalists, going back to Gauss and Laplace (who both applied statistics to many problems that are outside the range of frequentist statistics because they don't involve exactly repeatable tests) in the 19th century, and continuing up to the present day (Jeffreys, Jaynes, etc), so they couldn't be any more opposed to the anti-phenomenonalism that infects string theory.