It is traditional to end the U-Phil deconstruction discussion with the author’s remarks on the deconstruction itself. I take this from Wasserman’s initial comment on 7/28/12, and my brief reply. I especially want to highlight the question of goals that arises.
Wasserman:
I thank Deborah Mayo for deconstructing me and Al Franken. (And for the record, I couldn’t be further from Franken politically; I just liked his joke.)
I have never been deconstructed before. I feel a bit like Humpty Dumpty. Anyway, I think I agree with everything Deborah wrote. I’ll just clarify two points.
First, my main point was just that the cutting edge of statistics today is dealing with complex, high-dimensional data. My essay was an invitation to Philosophers to turn their analytical skills towards the problems that arise in these modern statistical problems.
Deborah wonders whether these are technical rather than foundational issues. I don’t know. When physicists went from studying medium sized, slow-moving objects to studying the very small, the very fast and the very massive, they found a plethora of interesting questions, both technical and foundational. Perhaps inference for high-dimensional, complex data can also serve as a venue for both both technical and foundational questions.
Second, I downplayed the Bayes-Frequentist perhaps more than I should have. Indeed, this debate still persists. But I also feel that only a small subset of statisticians care about the debate (because, they do what they were taught to do, without questioning it) and those that do care, will never be swayed by debate. The way I see it is that there are basically two goals:
- Goal 1: Find ways to quantify your subjective degrees of belief.
- Goal 2: Find procedures with good frequency properties.
If you think that Goal 1 is a good goal, you’ll be a Bayesian. If you think that Goal 2 is a good goal, you’ll be a frequentist. The debate is about which goal is a good goal. Once people decide which goal they think is the “right” goal, it is rare that they will change their minds. So if I downplayed the debate, it is probably because I am pessimistic about their being any real, open-minded debate (at least in statistics). But perhaps I am being too pessimistic.
Well, as I say, I agree with what Deborah wrote and I thank her for the interesting deconstruction. Now I’ll try to put myself back together.
–Larry Wasserman
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Mayo :
Larry: Your comment is provocative in a constructive way, since your laying out of goals gets to the heart of things (requiring much more than this little note):
“Goal 1: Find ways to quantify your subjective degrees of belief.
Goal 2: Find procedures with good frequency properties.If you think that Goal 1 is a good goal, you’ll be a Bayesian. If you think that Goal 2 is a good goal, you’ll be a frequentist. …Once people decide which goal they think is the “right” goal, it is rare that they will change their minds.”
Whether or not people change, they ought to care if these goals are:
(a) the only choices,
(b) obtainable, and
(c) if obtainable, desirable.
I don’t think these are the only choices, and would deny the first goal is obtainable in any way that would be desirable. But I only want to consider goal 2, because as a frequentist error statistician, you are saying that is my goal in life. It is not. Or rather, unless that goal is importantly qualified, it might at most be necessary and is not sufficient.A crucial qualification for scientific inference, as I see it, is that the error probabilistic assessments are relevant for indicating how well a given error (or erroneous interpretation of the data) has been probed (and perhaps ruled out) relative to the claim or interest, in the case at hand. Using error probabilistic considerations in this way is a day-to-day occurrence (e.g., learning about my weight right now, thanks to assessing what these scales are capable of in general).
If one claims the frequentist account is only interested in crass “behavioristic” low long run error rates (as ill formed as that goal can be), then we get stuck with howlers like the one in the link below.* Here, as in the Cox 1958 example, one reports a given, highly unreliable, measurement was actually reliable because with some probability a much better measuring tool might have been used, so on average it’s OK.
This whole issue of goals has immediate implications for the questions about assumptions that have arisen in responses to Wasserman these past few days, as well as for the central issues as to the viability of frequentist (error statistical) methods. Is it really an “either or”, or is this a false dilemma? I claim it is the latter, at least without an explanation of all that controlling long-run error rates provides. Many critics continue to unthinkingly repeat the charge that since these methods deal in long-run errors they are irrelevant for science. Entirely overlooked is what the long-runs entail about what is expected in the next set of trials, and how this information grounds what is absolutely essential for knowledge of reliable phenomena. Any method that is unable to supply such error control will fall short both over time and in the inquiry at hand.
Error Statistics Philosophy 