The Living Thing / Notebooks :

Bayesians vs frequentists

…and other interminable debates on how to do inference. Sundry schools thought in how to stitch mathematics to the world, brief notes and questions thereto.

Avoiding the whole damn issue

You are a frequentist and want to use a Bayesian estimator because it’s tractable and simple? OK. Discuss prior beliefs in terms of something other than probability, use the Bayesian formalism, then produce a frequentist justification.

Now everyone is happy, apart from you, because you had to miss your family’s weekend in the countryside, and and cannot remember the name of your new niece.

Frequentist vs Bayesian Acrimony

Was that too simple and practical? Would you prefer to spend time in an interminable and, to outsiders, useless debate? Is there someone you wish to irritate at the next faculty meeting?

Well then, why not try to use your current data set as a case study to answer the following questions: Can you recycle conditional probabilistic formalism as a measures of certainty for a hypothesis, or not? Which bizarre edge case can you demonstrate by assuming you can? Or by assuming you can’t? There are in fact more than two schools of thought here, and degrees within schools.

So far as I can tell, no-one waits to get a grip on such nuance before weighing in with an opinion though, so let’s keep that heading and mentally visualise the conflict in the usual way.

Myself, I can’t help but feel a lot of the confusion is terminological; If you accept Bayesian belief (as in, prior and posterior distributions) are not the same things as the probabilities frequentists use. (loosely, we expect something with P=0.5 to happen, over many experiments, half the time) you defang some constroversial claims. But this move is unpopular. I don’t get why.

Now, here is a sampling of actual expert opinions:

How it looks to me

OK, I have some data and a stochastic model with some free parameters. I’d like to know the plausibility, in some sense, of every possible configuration of parameters. A distribution of plausibility over distributions of probability. Neither school gets you that. Bayesians give you a best possible estimate given a “first guess”. Frequentists give your confidence regions for various parameter estimates based on a contrived notion of repeating a possibly unrepeatable thing. Both of these slice the infinitude of possible guesses in differently unsatisfactory ways.