What Should Philosophers Of Statistics Do?

D.G. Mayo looking scholarly.
A while back, far longer than it should have been, D.G. Mayo asked me to stop by her place and comment on a couple of posts. But laziness and excessive travel (primarily laziness) have kept me from doing so. This ungentlemanly behavior is partly corrected today.

Mayo bills herself as a “Frequentist in Exile”, a self-imposed state given her worry that subjective Bayesians have taken over most of the slots reserved for philosophers of statistics. She quotes from D.R. Cox, “arguments for this personalistic theory were so persuasive that anything to any extent inconsistent with that theory should be discarded” for an example the trouble frequentists are having.

Frequentist philosophers, mark you. Frequentists in practice outweigh Bayesians by at least an order of magnitude. P-values rain from the skies in both academics and in civilian life. And just try and teach an introductory statistics course which begins with or emphasizes Bayes and not frequentism and see where it gets you. Don’t guess: I’ll tell you. It gets you an invitation to take the first bus out of town. At least you can always run a blog where you beg for jobs (have any? See my Hire Me page).

But comparing miseries gets us nowhere. Let’s look at agreements.

Mayo is my sister in the mistrust of subjectivism. What an awful philosophy! What a distasteful way to found probability! “What’s probability? I’m glad you asked, Student. Truth is what gives you a special frisson, a shiver deep inside. If you want to know the probability, you must first tell me how you feel. Probability is completely personal. Your probability and my probability make us what we are.” Oh please.

Then again, I’m with Cox when he wants to jettison frequentism. Frequencies are the result of and may inorm probability, but they are not probabilities themselves.

There is a third way, which is so-called objectivism, all explained here: Subjective Versus Objective Bayes (Versus Frequentism). There are also fourth, and fifth, and etc. ways, all of which Mayo (if I read her right) and I don’t love. These for a long winter evening.


Nowadays, while the foundations of statistics are being considered anew by many statisticians, philosophers of statistics are almost nowhere to be found. Arguments given for some very popular slogans (mostly by non-philosophers), are too readily taken on faith as canon by others, and are repeated as gospel. Examples are easily found: all models are false, no models are falsifiable, everything is subjective, or equally subjective and objective, and the only properly epistemological use of probability is to supply posterior probabilities for quantifying actual or rational degrees of belief.

Amen and amen. All models are not false, and what a strange thing to believe: “Don’t trust me, I’m the statistician—what I just told you is false.” Of course some models are falsifiable: any time a model says X is impossible (as in impossible; a probability of epsilon is not impossible) and X happens, then the model is falsified; but if the model says the probability of X is epsilon and X happens, the model is not falsified.

Everything is not subjective: is the phrase “everything is subjective” subjective? I.e. true for thee but not or me? And everything can’t be equally subjective and objective: woe betide you if you know a truth but reject it for a feeling.

And “the only properly epistemological use of probability is to supply posterior probabilities…” isn’t quite right. That statement is only mostly true, which means it is sometimes false. It is false when there is no “posterior”, when we are “at the priori”, to coin a phrase. See the series linked above.

I’ll let Mayo have the last (and best) word.

There is a valid question as to whether it is the philosopher of X’s responsibility to solve philosophical problems in domain X; and the answer will surely depend on the field. But in statistical science—itself sometimes regarded as “applied philosophy of science,”—I say the answer is, emphatically, yes! Their failure to do so has left them out of one of the most interesting periods in the areas of statistical science as well as machine learning.


  1. William Sears

    As scientists – even statisticians – age they turn to philosophy.

  2. Ye Olde Statistician

    Where does Leonard Savage fall in this scale. I had just started reading his Foundations of Statistics and was intrigued by his use of decisions as mappings from a state space X to a consequence space Y. I did a master’s thesis on topological function spaces, and thought that if a topology (or proximity) could be defined on the consequence space Y, a derived topology (or proximity) could be placed on the decision space Y^X, developing a notion of when one decision is “close to” another decision.
    (Yes, I know. But general topology can be thought of as statistics without all the numbers.)

  3. JH

    [P]hilosophers of statistics are almost nowhere to be found.

    If philosophers of statistics want to be taken seriously by their statistician colleagues, imo, they need to first establish themselves as respectable statisticians who have actively kept up with recent developments in statistics.

    I think I’ve read some comments from Mayo on Gelman’s blog. I wonder if she considers Gellman, Draper and other well-known Bayesian statisticians, who have contributed to the philosophy of statistics, philosophers of statistics.

  4. Briggs


    Re: “kept up”. Does that include people who comments on blogs too?

    Re: “Mayo on Gelman’s.” Gelman is the guy who wants to bring p-values into Bayesian stats. Sheesh.

  5. Bill S

    Just a quick note that I scanned the blog and do wish I had time to get involved.
    Keep it up!

  6. Noblesse Oblige

    Will someone kindly explain to me why the philosophy project continues to go downhill, not uphill.

  7. Sander van der Wal


    Feynmann is saying what Popper is saying. And Popper was a philosopher. That should have the authority-angle covered.

  8. Rich

    N.O: “Will someone kindly explain to me why the philosophy project continues to go downhill, not uphill.”

    It’s seeking the point of maximum entropy. And entropy is uncertainty, sort of, and statisticians like uncertainty because without it they don’t have a job.

  9. JH

    Mr. Briggs,

    I don’t know what people who comments on blogs know and do in their life, though they probably need to use their brains to write comments. Do they study like a student? I don’t know. Anyway, it’s not easy to find a blog that keeps up to date with current statistics research, and such blog is usually written for specific audience. In addition to Gelman’s blog, here is another one that keeps one informed about recent developments on Bayesian data analysis, yes, including Bayesian p-values.

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