Last year I spoke at a conference celebrating the 10th anniversary of the University of Washington’s Center for Statistics and the Social Sciences, and just today a special issue of the journal Statistical Methodology came out in honor of the center’s anniversary. My article in the special issue actually has nothing to do with my talk at the conference; rather, it’s an exploration of an idea that Iven Van Mechelen and I had for understanding deterministic models probabilistically:

For the analysis of binary data, various deterministic models have been proposed, which are generally simpler to fit and easier to understand than probabilistic models. We claim that corresponding to any deterministic model is an implicit stochastic model in which the deterministic model fits imperfectly, with errors occurring at random. In the context of binary data, we consider a model in which the probability of error depends on the model prediction. We show how to fit this model using a stochastic modification of deterministic optimization schemes.

The advantages of fitting the stochastic model explicitly (rather than implicitly, by simply fitting a deterministic model and accepting the occurrence of errors) include quantification of uncertainty in the deterministic model’s parameter estimates, better estimation of the true model error rate, and the ability to check the fit of the model nontrivially. We illustrate this with a simple theoretical example of item response data and with empirical examples from archeology and the psychology of choice.

It says that the article was “Received 10 April 2009, Received in revised form 20 August 2009, Accepted 20 August 2009,” but the backstory is that we wrote and submitted the first version of this article around 1997 or so. It got rejected by several journals along the way, occasionally with reports that were encouraging enough to motivate us to add examples and clean it up in various ways. I still like the paper: even though it’s 13 years old, I think it has some important ideas which still are not fully understood, most notably the bit about checking the fit of the model nontrivially.

The special issue of the journal also features articles by Adrian Raftery (the founding director of the CSSS), Steve Fienberg, Don Rubin, Jon Wakefield, and many others.