Statistics

# Third Way Of Probability & Statistics Gets Comments

I just discovered a written comment, actually two, on my sketch-paper “The Third Way Of Probability & Statistics: Beyond Testing and Estimation To Importance, Relevance, and Skill“. Now when I say “I” I mean not I, but reader Bill Raynor. He directs us to the blog of Christian Robert, which I hadn’t known even existed.

Robert’s first comments ran along these lines (ellipses original):

[T]he document somewhat sounds like a practical (?) joke. And almost made me wonder whether Mr Briggs was a pseudonym…And where the filter behind arXiv publishing principles was that day.

The notion behind Briggs’ third way is that parameters do not exist and that only conditional probability exists. Not exactly a novel perspective then. The first five pages go on repeating this principle in various ways, without ever embarking into the implementation of the idea, at best referring to a future book in search of a friendly publisher…The remainder of the paper proceeds to analyse a college GPA dataset without ever explaining how the predictive distribution was constructed. The only discussion is about devising a tool to compare predictors, which is chosen as the continuous rank probability score of Gneiting and Raftery (2007). Looking at those scores seems to encompass this third way advocated by the author, then, which sounds to me to be an awfully short lane into statistics. With no foray whatsoever into probability.

Well, if “Mr Briggs” is a pseudonym don’t expect me to cop to it at this late date. I find it amusing Robert would have had Arxiv censor the paper. This is in accord with the best modern-day scientific practice of locking out the opposition.

Anyway, parameters don’t exist. If you think they do, find me one. I’ll wait here. Better, send me one in the mail. I’ll pay shipping. (I’m nothing if not generous. Incidentally, statisticians scarcely think about the origin of parameters.) Robert misreads me: I do not say “only conditional probability exists.” I say no probability of any kind exists. I say all probability is conditional; I also say all probability is epistemological. It’s true this is not a “novel perspective,” but my view does has the benefit of being true. I’ll take truth over novelty any day.

Incidentally, I have found a friendly publisher, as regular readers know. It was impossible in the sketch-paper to do more than sketch, which is why I refer to the book. I’ll let Robert know when it’s out.

How I derived the predictive distribution for the GPA example I thought too trivial to mention. It’s the standard, out-of-the-box Bayesian posterior predictive distribution for linear regression (which I referenced). And anyway, I have no particular love for that model. Use any model you like. I also don’t advocate the CRPS above all other scores. Indeed, as I insist, use the score that accords with the decisions you make with the probability model. Different people will thus—rightly—come to different views of the same model. Just like real life, eh?

The only real objection I have is Roberts’s last comment: “With no foray whatsoever into probability.” Brother, the exact opposite is true. My approach (old and not novel) is strict or pure probability. There’s no statistics to it, where by “statistics” I mean the ad hoc decision rules and other extra-probability procedures (Bayes or frequentist) used in the field. Instead of opaque models married to ritual, the “third way” emphasizes nothing but verifiable probabilities of observables, in which decision is identified as not probability, as it should be.

Somebody calling himself “coreyyanofsky” had this to say to Roberts’s post:

Briggs is an odd duck. His viewpoint, as near as I can tell, is a melding of Jaynes-Cox foundations and a kind of de-Finetti/Theodore-Geisser-style emphasis on predictive inference. I think he thinks that only observable quantities “deserve” to get probability distributions.

I object to the term “odd duck.” That’s odd drake, fella. I will plead guilty to plotting from the Duke & Drake to overthrow the old ways of doing statistics, though.

The rest of the comment is accurate, and even though Theodore Geisser is almost the right name, perhaps Theodor Geisel is more appropriate. I even approve of the scare quotes around “deserve” (as will be clear from my remarks above).

I mentioned two comments by Robert. The second came in a recent talk he gave (in slides 8 and 9). In slide 8, after inappropriately putting scare quotes around the word true, he mentions posterior predictive methods, which is good (though I don’t advocate Gelman’s use of Bayesian posterior p-values).

On slide 9, after sliding back in the old way of thinking of things, he says there is no “third way.” Which I take as an indicator that my perhaps pseudonymous paper got under his skin. He does say a “shift” in thinking is needed. Amen to that. A shift to a third way.

My book should be out June-ish.

Categories: Statistics

### 27 replies »

1. John B() says:

even though Theodore Geisser is the right name, perhaps Theodor Geisel is more appropriate

Stole my comment: “Did he mean Dr. Suess?”

2. Briggs says:

John,

Actually, I think he meant Seymour Geisser. According to Wiki:

Seymour Geisser (October 5, 1929 — March 11, 2004) was a statistician noted for emphasizing the role of prediction in statistical inference. In his book Predictive Inference: An Introduction, he held that conventional statistical inference about unobservable population parameters amounts to inference about things that do not exist, following the work of Bruno de Finetti.

Geisser was right.

Update Here’s a paper which interviews Geisser. Some nuggets there.

3. Gary says:

One Fish Two Fish Red Fish Blue Fish.

What’s the probability of that? 😉

4. Dear Dr. Briggs:

Better get used to this kind of idiocy – at least this one didn’t get too deeply personal.

My series on IBM mainframe Linux drew over 3,000 pieces of hate mail – including one delivered by fedex on a senior CIO’s personal stationary. Like your friend here, however, they were all wrong and that’s what you should remember when dealing with them.

5. Briggs says:

Paul,

The only thing I seriously object to is the outfit Robert wore in front of Oxford students. This documentary evidence proves the French are not inherently more fashionable than Americans. Can anybody make out what the t-shirt reads? “I love parameters” maybe?

6. Can’t wait for your book!

I am constantly fascinated by the similarities between probability, prediction and psychics. While the first two are “scientific” and the last is “not”, in reality they all work toward the same goal. Some methods and individuals are more successful than others, as is expected. All are trying to predict—or put more succinctly, to see the future and know it. Fascinating how the two are so similar and both in goal and in success levels. Equally interesting is how one group is considered science, the other pseudoscience. Pretty much, it’s all weaving between science and philosophy. If both sides just admitted this, it would be very helpful and at least honest. (I’m not holding my breath on that, of course.)

Gary: I doubt mathematics, statistics or psychics could predict your comments! You’d have them all stumped!

7. John B() says:

Briggs

Re: T-Shirt

Near as I can make it out:

RACCOON RIVER BREWING CO.

8. JohnK says:

Instead of opaque models married to ritual, the “third way” emphasizes nothing but [not ‘by’] verifiable probabilities of observables

I ask you to do this because the paragraph in which it is nested is such an apt summary of your project and your critique, and it would be nice if it read correctly as well.

I continue to marvel at the merely-glancing encounters with your argument that appears to be the maximum some professional statisticians appear to be able to achieve. Almost as if their education and daily work has trained them to automatically steer themselves away from thoughts like yours. That your arguments even prompt ridicule or dismissive categorization in some small number of those minds is then a kind of victory, if a meager one.

I am reminded of looking in one edition of Bernard Rosner’s well-known biostat text, where he says on one page that “we cannot say” what any particular confidence might mean, and then spends the next 200 pages pretending that we can.

But as Paul Murphy mentions in his comment, don’t take it personally. We are – all – not very good at thinking things through, particularly when what we ‘know’ ain’t true.

9. Briggs says:

JohnK,

My enemies went for the typo subtle today.

10. Gary says:

Sheri, 60+ years of observation feeds free association.

11. Briggs says:

Fred,

Thanks. Love the Feynman quote! Too bad that today it’s taken seriously.

12. Steve E says:

“I continue to marvel at the merely-glancing encounters with your argument that appears to be the maximum some professional statisticians appear to be able to achieve.”

JohnK, I have recently gone all-in and invested all available capital in fainting couches in anticipation of Briggs’ book.;-)

13. Fred says:

Thanks Briggs, I really can’t overstate its importance…unfortunately it usually falls on deaf ears!

14. JH says:

What is “pure probability”? What kind of “pure probability” is involved in data (statistics) modeling? (Yes, those are scare quotes in my question.)

It really doesn’t matter whether those quotes are appropriately placed or are scare quotes in Robert’s slide. I can see why he places them on the word “true.” I studied one of Robert’s books last summer. He has the view that models are at best approximations of reality, and his model choice philosophy does not aim at finding “true model” (or “true answer” as stated in your third way paper). He explains that the core of Bayesian analysis is to provide inferences conditional on the realized data.

Robert’s criticism doesn’t necessary imply that he disagrees with you on the nature of parameters and conditional probabilities. His points are that your views are not new because researchers are looking for new ideas, and that your presentation of the example in the paper is sloppy. His criticisms may not be kind, but they are valid, imo.

15. Briggs says:

JH,

Sloppy, eh. But you have confirmed the ancient wisdom that a man knows he’s won an argument with a woman when all she has left is, “It’s not what you said, but the way you said it.

Death to hypothesis tests!

16. “I find it amusing Robert would have had Arxiv censor the paper. This is in accord with the best modern-day scientific practice of locking out the opposition.”

‘Puts to bed the old snide canard about science allowing criticism unlike religion. If anything, science is far more guarded about its sacred cows than even Islam.

17. Paul W says:

This is in the text of the link:
” With my Racoon River Brewing Co. tee-shirt I brought back from Des Moines.”

Was a great local place with good beer, but unfortunately it’s now closed.

This is confusing:

“I say no probability of any kind exists. I say all probability is conditional; I also say all probability is epistemological.”

No probability exists but all probability is epistemological. Does this mean probability doesn’t exist like random chance doesn’t exist? Probability is therefore only a measure of the accuracy of knowledge represented by a model?

18. JH says:

But you have confirmed the ancient wisdom that a man knows he’s won an argument with a woman when all she has left is, “It’s not what you said, but the way you said it.”

I am glad you feel that you have won a argument. So what is the argument you have won? Well, I will settle for answers to my questions above.

Hahaha. Let me offer you another nonsensical wisdom- “A woman knows she’s won an argument with a man when all he can do is to move the goalpost.

19. Briggs says:

Paul W,

20. acricketchirps: Of course not.

21. Paul W says:

You can’t squeeze blood out of a turnip.

22. Mactoul. says:

Sheri,
“All are trying to predict”
One may mark out science from non-science, not by the aim but by the means to the aim.
The non-sciences do not “predict” in the sense the sciences do. In sciences one computes using a procedure and in such a way that a lot of data is required to output a prediction. A sort of conservation of information.
Non-sciences, such as astrology require very little input data but are able to “predict” a lot of things. Essentially, their output is indefinitely large.
Psychics on the other hand use no algorithm at all. A better word for their activity would be prophecy.

23. tom0mason says:

“Anyway, parameters don’t exist. If you think they do, find me one. I’ll wait here. Better, send me one in the mail. I’ll pay shipping. (I’m nothing if not generous. …)”

Well I had a few hundred tons of parameters to ship to you, but the shipping company insisted I boil them down to fit in the container, upon which I noted they amounted to nothing — not even zero! Well I be …

🙂

24. John B() says:

Re: Feynman Quote and previous posts about Physics

Wouldn’t that make Physics more “accessible” Social Justice-wise?