Setting:

The situation here is the following: We want to estimate the probability of tumours in a control group of type "F344" rats. In our latest experiment, we have fourteen rats ($n = 14$), and we observe four tumours ($y = 4$).

Additionally, we have historical data from seventy previous experiments, which we can use to inform our model. In total, we have $x_i = 71$ total experiments with $n_i$ rats, and $y_i$ tumours, with $x_{71}$ being the experiment of primary interest.

Models:

NumPyro code can be found here.

Turing code can be found here: (TBD)

The Dataset:

We have the following data from Tarone (1982) via BDA3: