It’s usually more involved than this. I don’t know why everyone wants to do this. Andrew’s theory is that people in engineering are trained to look at a lot of problems as data transforms rather than generatively.
Here’s the latest example, which was literally the last message to which I responded before this one:
Presumably the function f they’re using is more complicated than addition, but it presents exactly the same problem.
In the IRT section they fiddle around with a bunch of this stuff because the model’s not identified. Just to be clear, you do not and cannot do what they do in BUGS in Stan—I show that and explain why in the manual chapter on problematic posteriors. I’m not even convinced what Gelman and Hill are doing works in BUGS—they never validated it and the guarantees for Gibbs all go out the window with improper posteriors as you don’t even have a density from which to sample!