I’ve made this point before, but I just received an email on the topic and so I thought I’d point youall to section 3.3 of this article of mine from 2003 where I make the argument in detail.
This article–A Bayesian Formulation of Exploratory Data Analysis and Goodness-of-fit Testing–is one of my favorites. It also features:
- A potted history of Bayesian inference (section 2.1)
- The first published definition (I think) of U-values and P-values (section 2.3)
- A model-checking perspective on the problem of degenerate estimates for mixture models (section 3.1)
- Why this isn’t all obvious (section 5)
The article is based on a presentation I gave a year earlier at a conference. It was supposed to appear in the proceedings volume, but it was late, and the conference organizer was so annoyed he refused to include it. So I published it in the International Statistical Review instead. A year later I published a related article, Exploratory Data Analysis for Complex Models, as a discussion paper in the Journal of Computational and Graphical Statistics. That second article is more coherent, but personally I prefer the International Statistical Review article because it covers so many little topics that don’t fit into existing theories of inference. I think of these examples as analogous to the quantum anomalies that toppled classical physics around 1900. In this case, what I want to topple is classical Bayesian inference–by which I mean Bayesian theory that does not include model building and model checking.