More about WAIC

[oliviergimenez]

I find my section on WAIC weak, and I definitely need to do better. Among other things:

• I don't talk about marginal/condition WAIC and grouped data (e.g. https://groups.google.com/g/nimble-users/c/VqTyosXi4Sk/m/Gs5zZ_N3AwAJ)
• I do not use WAIC much in the rest of the book (but I'll use it more in case studies I guess); could e.g. compare WAIC of model with flood/nonflood with constant and time-dep models
• I don't introduce WAIC weights anywhere, maybe to be done in a case study
• There's also the elephant in a room, shall we go for model selection (à la Burnham), or just fit a big model (à la Gelman) and go from here.
• For now, I'm also ignoring cross-validation, see https://avehtari.github.io/modelselection/CV-FAQ.html and this excellent post by Vehtari https://statmodeling.stat.columbia.edu/2022/06/30/47790/.
• Make sure I refer to RJMCMC when I talk about WAIC, and vice-versa.
• See also this thread and that one, and the diff bw variable and model selection.