Breaking through ‘the breakthrough’
A reader sends me this excerpt from Thomas Leonard’s “Bayesian Boy” book or diary or whatever it is:
“While Professor Mayo’s ongoing campaign against LP would appear to be wild and footloose, she has certainly shaken up the Bayesian Establishment.” Maybe the “footloose” part refers to the above image (first posted here.) I actually didn’t think the Bayesian Establishment had taken notice. (My paper on the strong likelihood principle (SLP) is here). *This falls under “rejected posts” since it has no direct PhilStat content. But the links do.
Rejected Posts of D. Mayo 
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Portions read like an autobiographical memoir recording disappointments with Bayesian mentors. He writes, “I also took time to revise my philosophies of statistics,… It finally dawned upon me that the Bayesian approach is quite incomplete because it requires the mathematical and probabilistic specification of a sampling model, and cannot usually be used to derive suitably meaningful models from the data.” Poor (Bayesian) boy.
It’s kind of spooky how people can take pictures from your blog and use them in any way. Why, in discussing J. Berger in chapter 6 http://www.thomashoskynsleonard.co.uk/bayesian_boy6.htm
(there are no pages) would the author use a picture of Berger with me in it? (taken when I invited him to speak at Virginia Tech, and posted when I was “deconstructing” a Berger paper on my blog).
It’s interesting how different mathematical fields choose to focus more on logic vs. set theory; metalogic (or metamathematics) vs.mathematics; probability logic vs. statistical mathematics.
In one entry he writes: “26th August 2013: I have now heard from Peter Wakker that Evans, Fraser, and Monette (Canadian Journal of Statistics, 1986) claim that the Likelihood Principle is a direct consequence of the Conditionality Principle, and that the Sufficiency Principle is not needed at all. Phew!”
The thinking is (and he is not alone) that taking away a premise could save the original derivation since it’s “weaker”, but it’s the reverse:
If (A implies B) then ((A and C) implies B) so if the latter implication fails, then so does the former*. It’s obvious once you think about it for a second, but I understand it’s not front and center while immersed in mathematical statistics. Conversely, many philosophers are prepared to juggle very complex logical tools–even with probabilities–, yet are distant from mathematical statistics.
*Of course there are non-monotonic logics, but that’s not relevant here.
Dr. Mayo, it’s true that
(A implies B) implies ((A and C) implies B)
is a tautology. But that’s not what’s at issue. The goal is to know the truth of B.
If ((A and C) implies B) is a theorem (i.e. is True) then you have to know that both A and C are true to conclude that B is true. That’s because there’s a possibility that A=True, C=False and B=False, which would still make the theorem true.
On the other hand, if (A implies B) is a theorem (i.e. is True) then you only have to know that A is true for B to be true.
So it’s a “weaker” theorem in the precise and useful sense that we have to know less in order to get at the truth of B.
On a general note, mathematical logic is a standard part of undergraduate mathematics curriculums. I understand Philosophers are rightly proud of their work in logic, but slamming math types for their failure to understand logic is guaranteed to backfire. If they didn’t understand logic they wouldn’t last two seconds as a math major.
Sure it’s weaker, but if it’s possible to have [(A & C) & ~B], then it’s possible to have (A & ~B). I was a double major in math and philosophy, and did indeed have some logic in both. I certainly wasn’t slamming anyone–that’s rather an over exaggeration of what I said (which actually was something said to me by some excellent statisticians). There’s a difference in language in some ways. But there’s more involved in this (SLP) issue of a logical nature (having to do with quantifiers) that, once translated, makes it look too distant from math/set theory (and statisticians are tend not to want to read it). Still,I think philosopher’s of probability who are distant from mathematical statistics are at much more of a disadvantage.
We have quite a few “anons” on this blog, perhaps they should take different numbers….
Anon: By the way, a statement’s being true is not the same as its being a theorem. I assume you meant to say “z is a theorem (i.e., z is a logical truth)”–true in all models (of the logic). That holds so long as the formal system is complete and consistent, (as I take it the logic we’re dealing with is).
Leonard’s memoirs are fascinating. He seems to have fallen into Bayesian statistics by accident. ” Professor David Cox’s course in Statistics was however quite inspiring. By the time I graduated, he and his colleagues were to give me a solid grounding in classical Fisherian/ Frequentist statistics that provided a basis for my entire career. Indeed, I still regard myself as a Fisherian at heart, despite the influences of the Bayesianism that was forced upon me in 1970 when I needed an S.R.C. grant to study for my Ph.D.” He has done a lot of work in the trenches on applied Bayesian techniques, but has not been averse to pointing out problems, with much damage to his professional career, if he is to be believed. His book with Hsu on Bayesian statistics is very useful even if not very readable.
David P: Thanks for your comment. I know nothing about L. Thomas except that we had some e-mail exchange awhile back on the likelihood principle.after which he wrote some comments on this blog that were off. Still, 3 people that I know alerted me or sent me this memoir, so I decided to mention it on this blog. I routinely e-mail people referenced on my blogposts (as I find welcome in reverse), but Thomas’ reaction Sat. was to issue a bizarre array of hostile accusations against me, along with threats (to inform my dept. head that I referenced a quote from “Memoir of a Bayesian Boy” thereby making me guilty of “plagiarism”). Very strange.
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