I received this query from a reader and thought it important enough for all of us to answer.
I was hoping you could provide some advice for an aspiring statistician. I am an undergraduate in math preparing to apply to graduate school in statistics, and I love studying the subject and analyzing data. However, I am now convinced by the arguments against classical statistics and I fear committing to a career path where I will be forced to participate in hocus-pocus. Is there an intellectually honest way forward? For instance, are there particular statistics departments doing things right? And if I can’t get accepted into / afford any of these schools, should I just do something else?
I’d greatly appreciate any guidance you can give.
I do not know any graduate department that will allow you to bypass classical methods. It’s true there are some departments that are greatly sympathetic to Bayesian statistics, but Bayes must always come after frequentist; even in “Bayesian” departments it’s an add-on. Anyway, many of the same mistakes in philosophy are made in Bayes as they are in frequentism.
Idea is to eschew standard statistics departments and come at the subject sideways.
You can consider going the straight mathematical route. Choose a math department which will allow you to do probability. Not much data analysis that way, and the (of course) over-emphasis on probability as mathematics, which means you can begin to forget that most probabilities aren’t quantifiable. On the other hand, you can focus on what I think will be a huge area for observable predictive statistics: combinatorics.
Since all measurements are finite and discrete, and no measurement can in reality go to infinity, all probability is finite and discrete, or should be, which makes figuring problems exercises in combinatorics. Learn to count. You can do the math without telling statisticians that you’ll eventually use it for statistics. The mathematicians won’t care.
Applied math is a good option. But even in applied math the focus will be on parameters and parameter analysis, which we agree leads to over-confidence or fallacy. There are many mathematical tools statisticians use that you’ll only gain a passing familiarity with unless you’re in a stats department, but most of these are in “estimation” theory, which always means estimating unobservable parameters about which we should have very little interest. But if you’re a mathematician, you’ll be able to figure these out when you need them.
Another good option is physics. I’d recommend this as the ideal option, but I’m guessing you haven’t done much undergraduate work in the area, which puts you at a major disadvantage. It’s not a coincidence that many advantages in predictive probability and even the philosophy of probability have come from physicists.
Physicists used to emphasize observables in all its branches, but even there that trait beginning to slide. Yet you can avoid the weirdness by staying away from string theory, multiverses and the like.
And then there’s philosophy itself. That would be the toughest place to break in, but only because not a lot of departments do much probability. Many do philosophy of science, naturally, and those would be the places to look. Philosophers are more willing on average, and not surprisingly, to welcome argument on received wisdom. This isn’t so in many other areas of science.
If you want to go to any school or department, first discover the kind of work you think you’d like and then find somebody who is doing it. Write them and see if he needs students.
The last option is to skip school all together and teach yourself what you need. Takes a lot of dedication, but it can be done. Problem is your potential employers, either because they’re too lazy to assess skills of potential employers or because they are forbidden to do so because of government threats (diversity), often want certification.
What does everybody else have to say?