I would like to train models using Bayesian Inference (for example using NUTS), so that there are coefficients working at different levels. This is an example:
level 1 | level 2 | a0 | a1 | y A | A1 | 1.0 | 1 | 10 A | A1 | 9.2 | 0.9| 13.2 A | A2 | 1.3 | 1.1| 13.4 A | A2 | 1.4 | 1 | 12 B | B1 | 1.0 | 2 | 9 [...]
I would need a way to train linear models to predict y. The trick here: I need a0 and a1 to be trained at different levels: I need a coefficient for a0 for each different level 1, and a coefficient for a1 for each level 2.
Any idea how I can write such a model with Pyro?