MOVED: Reflections on the Paradigm Change (2/1/12): NEW ADDRESS: http://errorstatistics.com

Dear Reader: (Wed. noon):  Well we've moved, in the sort of piecemeal, unsettled manner that I suppose the error statistical philosophy favors: take the leap first, then be compelled to adjust by trial and error stress tests afterward.  As with all such progressive changes, while some of the old problems are solved, new and deeper problems appear; things that were easy to explain in the old paradigm are no longer explicable (as of yet), and some activities that were problem-free and predictable before, are now filled with puzzles and uncertainties.  I'm not throwing out this glorious old typing machine just yet however...it still serves in some areas as a kind of limiting case, and standard, when the exactitude of the new paradigm is scarcely needed.  Well, see you over there...Taking a day off to unpack all those boxes that the moving people brought over to errorstatistics.com this morning.
Best, Mayo

Dear Reader: Tuesday evening:
Well, I lied, because I'm back to using my trusty old machine while snafus with the new, improved platform are ironed out--and isn't it lucky that I didn't take it out with the trash this afternoon?  If you wish to post any comments, solutions to the riddle, or share condolences, you may still post here.  Sorry.
D. Mayo

Dear Reader: (Tues. a.m.)
Well this is my last post typed out on this old thing. I thought it perfectly good actually, even though this keyboard is a bit rusty and the fonts often have a mind of their own; I shall miss it.  You will laugh to hear that a representative from Elba actually had to fly all the way to the U.S. to ensure I’d finally stop dithering and move to the new-fangled blog site that currently exists as an alternative universe (until we turn it on).  My Elbian friends know all too well that in situations like these I have a tendency to display what Nietzsche calls the Russian Fatalism:

 “by tenaciously clinging for years to all but intolerable situations, places, apartments, and society, merely because they happened to be given by accident: it was better than changing them, than feeling that they could be changed.” (Ecce Homo, I think it’s Why I am So Wise)

Anyway, as my last little puzzle from here, you may have noticed a caption under the picture of Elba (on this page) for the past several weeks (although no one has mentioned it):

able no stats on Elba

What is interesting about this phrase do you spoze?  You only have today to answer (for a w-point).

Yours Sincerely,

D. Mayo 
P.S. CLICK ON PICTURE OF PINK WASHING MACHINE TO GET IMMEDIATELY TO NEW SITE

Moving Day TODAY!

We are in the process of moving the Error Statistics Philosophy Blog (including all previous posts and comments) to a new platform. 

Our understanding is that the Word Press platform provides for a better reader experience and commenting should be much quicker and easier.

Starting today (January 31), you will be able to find us at:

http://errorstatistics.wordpress.com/

We hope to see you there.  Best, the Sailor from Elba

No-Pain Philosophy: Skepticism, Rationality, Popper, and All That: The First of 2 Parts

I want to shift to the arena of testing the adequacy of statistical models and misspecification testing (leading up to articles by Aris Spanos, Andrew Gelman, and David Hendry).  But first, a couple of informal, philosophical mini-posts, if only to clarify terms we will need (each has a mini test at the end).

1. How do we obtain knowledge, and how can we get more of it?

Few people doubt that science is successful and that it makes progress. This remains true for the philosopher of science, despite her tendency to skepticism. By contrast, most of us think we know a lot of things, and that science is one of our best ways of acquiring knowledge. But how do we justify our lack of skepticism? Any adequate account of the success of science has to square with the fact of limited data, with unobserved and unobservable phenomena, with theories underdetermined by data, and with the slings and arrows of the threat of error. Intent on supplying such an account, I’m drawn not toward some ideal form of knowledge “deep down,” nor toward some perfectly rational agent, but simply toward illuminating how in fact we get the kinds of knowledge we manage to obtain—and how to get more of it!

As such, the centrally relevant question is: How do we learn about the world despite threats of error?

2. Inductive inference as “Evidence Transcending”

The risk of error enters because we want to find things out—make claims or take action—based on limited information.  When we move beyond the data to claims that are “evidence transcending,” the argument, strictly speaking, is inductive. The premises can be true while the conclusion inferred may be false—without a logical contradiction. Conceiving of inductive inference, very generally, as “evidence-transcending” or “ampliative” reasoning frees us to talk about induction without presupposing certain special forms it can take.  Notably, while mathematical probability arises in inductive inference, there are two rival positions on its role:

·      to quantify the degree of confidence, belief, or support to assign to a hypothesis or claim (given data x); and

·      to quantify how reliably probed, well-tested, or corroborated  a claim is (given data x).

This contrast is at the heart of a philosophical scrutiny of statistical accounts. 

Confusion about induction and the threat of the so-called philosophical problem of induction have made some people afraid to use the word—even statisticians, who could in fact be teaching philosophers about it.  Such fears, however, are unwarranted, once it is properly understood.  But more important, even those who claim to restrict themselves to variations on “deductive” falsification must warrant their premises empirically, as that arch falsificationist Karl Popper knew only too well.

3. Popper, Probabilism and Severe Tests

Since Popper keeps popping up in the statistical literature (e.g., in Stephen Senn, Andrew Gelman), let me try without philosophical fanfare to say something about him.  In one sense Popper was a skeptic: he didn’t think we could justify hypotheses as either true or probably true—he rejected “probabilism” (also called “inductivism,” which is confusing).  Yet he still thought science was successful and that there were rational methods of science.

Consider the two views of probability just given. The first view, that probability arises to assign degrees of belief, truth, or support to hypotheses, goes hand in hand with the conception that claims are warranted by being either true or probable.  Popperians also call this probabilism or justificationism, and we can retain those terms. When it is said that Popper was an anti-inductivist, what is really meant is that he rejected probabilism.  He did not reject the idea that it was possible to warrant evidence-transcending claims.  Instead, he required that evidence-transcending claims be accepted (or preferred, or inferred) only if they have been subjected to, and have passed, stringent tests. Probability, accordingly, arose in the second sense.   Here, probability is best seen as characterizing the properties of a method or rule, which we may call a method of testing.   

For example, a good testing rule might be one that with high probability would falsify a hypothesis H if false, but not otherwise. For Popper, a hypothesis was well corroborated only to the extent that it passed a severe attempt to falsify it. 

4. The Wedge between Skepticism and Irrationalism

This focus on using probability to qualify testing methods (rather than claims) is the key that allowed Popper to “drive a wedge between skepticism and irrationalism”. (e.g. Musgrave  1999, p. 322).  We can be skeptics about inductively inferring that H is probable---we can reject probabilism outright---while still allowing warranted inferences to H.  We need only have rational testing methods or rules.

We can allow

It is warranted to infer H

to be open to including any number of epistemological stances: It is warranted to infer (believe, accept, prefer, act in accordance with) H. 

          Popperians oust probabilism but retain rationality by defining rationality as following a rational method. A rational method is one that infers (or claims to have evidence for) H only to the extent that H has passed a severe test---a test which would have, with reasonably high probability, detected a flaw in H, were it present.[i]

          Popper often viewed hypotheses as “solving problems” –where the problem could be construed very generally.  So we might say that an irrational method is one that would, with high probability, declare our problem solved, when in fact it was not (or not solved to a degree specified). Such a method would to readily declare the problem solved erroneously.

          Popperians escape the need to come up with a logic of (or methods for) confirmation—but they still need methods for severe tests, and ways to evaluate tests on their error-probing ability.  Can this be achieved?   Stay tuned.

 _______________________________________________

Mini-Test:

What are the two uses of probability in inference?

How does Popper drive a “wedge” between skepticism and irrationality?

What is probabilism (or justificationism)?

What would be an irrational method for solving a problem?

 ____________________________________________

Lakatos, I. 1978. The Methodology of Scientific Research Programmes. Edited by J. Worrall and G. Currie. Vol. 1 of Philosophical Papers. CUP.

Mayo, D. 1996. Error and the Growth of Experimental Knowledge. Chicago: University of Chicago Press.

Mayo, D. 2011. “Statistical Science and Philosophy of Science: Where Do/Should They Meet in 2011 (and Beyond)?”  Rationality, Markets and Morals (RMM) Vol. 2: 79-109.

Musgrave, A.  1999. Essays in Realism and Rationalism. Amsterdam: Rodopi; Atlanta, GA.

Popper, K. 1959. The Logic of Scientific Discovery. New York: Basic Books.

Popper, K. 1983. Realism and the aim of Science.  NJ: Rowman and Littlefield.

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 “Mere supporting instances are as a rule too cheap to be worth having…any support capable of carrying weight can only rest upon ingenious tests, undertaken with the aim of refuting our hypothesis, if it can be refuted (Popper 1983, 30).