14.3 Data augmentation
See maybe here https://www.math.unm.edu/~fletcher/PDF/PUB-PDF/SANDER.PDF and maybe, but probably not, here https://staffblogs.le.ac.uk/bayeswithstata/2015/04/10/poisson-regression-with-two-random-effects-mcmc-by-data-augmentation-part-ii/
Note to self: See ChatGPT answer :)