Posts Tagged With: conflicting foundations

U-Phil: (concluding the deconstruction) Wasserman / Mayo

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. Continue reading
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Dennis Lindley’s “Philosophy of Statistics”

Philosopher’s Stone

Yesterday’s slight detour [i] presents an opportunity to (re)read Lindley’s “Philosophy of Statistics” (2000) (see also an earlier post).  I recommend the full article and discussion. There is actually much here on which we agree.

The Philosophy of Statistics

Dennis V. Lindley

The Statistician (2000) 49:293-319

Summary. This paper puts forward an overall view of statistics. It is argued that statistics is the study of uncertainty. The many demonstrations that uncertainties can only combine according to the rules of the probability calculus are summarized. The conclusion is that statistical inference is firmly based on probability alone. Progress is therefore dependent on the construction of a probability model; methods for doing this are considered. It is argued that the probabilities are personal. The roles of likelihood and exchangeability are explained. Inference is only of value if it can be used, so the extension to decision analysis, incorporating utility, is related to risk and to the use of statistics in science and law. The paper has been written in the hope that it will be intelligible to all who are interested in statistics.

Around eight pages in we get another useful summary:

Let us summarize the position reached.

(a)   Statistics is the study of uncertainty.

(b)    Uncertainty should be measured by probability.

(c)   Data uncertainty is so measured, conditional on the parameters.

(d)  Parameter uncertainty is similarly measured by probability.

(e)    Inference is performed within the probability calculus, mainly by equations (1) and (2) (301).

Continue reading

Categories: Statistics | Tags: , , , | 50 Comments

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