Update: See this post on the definition of confidence and credible intervals.
Submitted for your approval, a new paper. A polemic describing in nascent terms the paradise that awaits us once we cease teaching frequentist statistics to non-statisticians. This Great Bayesian Switch is to occur in August of 2013.
The paper is already in the hands of editors and referees at American Statistician, a general interest journal issued by the American Statistical Society. But the paper has also appeared on Arxiv (arXiv:1201.2590v1), a repository for “preprints” submitted by those who have passed the weak test of being recommended by other Arxiv authors.
(If I were able to draw, the graphic that would accompany this post would feature R.A. Fisher putting on his hat, suitcase in hand, heading out the door and casting a sidelong glance at the Rev. T. Bayes, who is looming in the foreground, a beatific, Mona-Lisa smile on his face.)
It is written to be understood and spoke to by trained statisticians, especially those that teach this grand subject. But all are welcome to read it. Be forewarned that if you do not know the precise, technical definitions of p-values and confidence intervals, information that mystifyingly appears to be well guarded secrets, then you will gain little from reading this paper.
My reasons for calling for the Bayesian Switch are outlined in the paper, so I won’t repeat them here. You may ask what are the chances that its recommendation will be implemented, and I will answer: somewhere well south of the chance that the EPA decides it has regulated its citizens enough and returns its budget unspent to Congress. The retort is: you have to start somewhere and my hope is that this paper will start a discussion (the probability of that is also low, I’m guessing).
I anticipate (from experts) a few counter arguments, which I peremptorily answer here:
You are claiming that Bayes is superior to frequestism?
Are you saying those that hold with frequentism are bad people?
But you are claiming that a theory I happen to believe is wrong. This is rude.
It is not.
Even if Bayes is better—and I say it isn’t—then professional statisticians who use frequentist techniques do a fine job.
Then what is your problem?
Most statistics are done by non-professional statisticians, and those that use frequentist techniques arrive at a level of certainty in their results that is unwarranted. This is because they fail to understand (or remember) what the results mean within frequentist theory. Plus, nearly everybody, including not a few statisticians, interpret frequentist results in Bayesian terms. We should eliminate this confusion.
They do not.
But they do. I challenge you to find me in any published statistical analysis, outside of an introductory textbook, of a confidence interval given the correct interpretation. If you can find even one instance where the confidence interval is not interpreted as a credible interval, then I will eat your hat.
This isn’t fair. Confidence intervals are tricky things; even Neyman had difficulties defining them. Anyway, most people don’t use them.
True. They use p-values. Do you really want to rehash that discussion?
Look here. It’s too much trouble to change. Coordinating such a thing would be impossible. All my slides are already made up! The books are already ordered. Exams are written. And I don’t mean mine. Do you know of all the frequentist statistics questions that are asked everywhere, from medicine boards to bar exams?
You have me there.
Well, then, that’s fine. It’s good to see even you can be reasonable.
Even if everybody can’t change, you can.
I won’t. Because I suspect that you have ulterior motives in your Great Switch beyond just teaching a simple theory of probability.
I do. I would eliminate forthwith the peculiar and misplaced focus on parameters that is the basis of both frequentist and most Bayesian analyses. This is the true source of rampant over-confidence that plagues science. If we required people to speak, instead of unobservable parameters and unverified assertions, but of tangible, measurable objects, then we would cut in half the flow of nonsense. I’m so confident of the correctness of this view, that I’ll even let you have the last word.
And I’ll take it. You are out of your mind.