Coherence, charity and triangulation in statistical modelling

Abstract

Bayesian statistics rests on a few familiar distinctions: frequentist vs. Bayesian, objective versus subjective probability, a model versus the data it is fitted to, a prior versus a posterior. Here, I use Donald Davidson's "third dogma of empiricism" to critique such distinctions in terms of scheme/content dualisms. With a single running example -- estimating how often a football (soccer) team scores -- I argue that a degree of belief is in itself objective, that model and data are better seen as parts of one belief system than as different kinds of things, and that Bayes' theorem describes relations within that system rather than data updating a model from outside. What matters instead is how belief systems are built, checked and rebuilt. To this end, I use Davidson's constructive programme of radical interpretation to suggest that a belief system should be not only coherent (as statisticians already require) but also charitable and triangulated, answerable to other people and to a shared world. I argue that these three constraints are exactly what good statistical practice -- from eliciting priors to checking models -- already tries to satisfy and talking about them explicitly could improve this practice.