PyMC multiple observations examples

PyMC_Multi-Obs_Examples.ipynb

Notes

The problem setting I am facing is after conduct an experiment, there doesn't seems to be the defacto way of training the new model since multi observations is removed after PyMC 3. This problem is related to casual modeling as it is often use to test counterfactual outcome, There is this awessome CausalPy package which can analyze the trained model, and ask for counterfactual outcome. But they didn't specify how to update the model. So I created, and tested on a toy dataset on the model to see if this works (And it did)

However I tried apply Gaussian Process using pm.gp.Latent, and pm.gp.HSGP both sampling diverge. But I still haven't tried Gaussian Random Walk, but on my separate experiment GRW is too flexible, and making other learnable parameters to not converge (rhat > 4)

The method I tried here modeled after gaussian spline (Orbit KTR), and linear spline which (Prophet, and Orbit KTR). But it is possible to model time varying coefficients using more parametric means such as linear, logarithmic, or logistic