Hierarchal Bayesian Modeling

Gist

There’s some structure of the data

Definition

Given that that there is an observations $y_i$ and the parameter ${\theta }_j$ that governs the data-generating process and a hyper parameter ${\varphi }_j$, then Step 1:

Then stage 2:

Then Stage 3:

Hyperparameters

Parameters describing the Priors

Hyperpriors

Distribution of the

Pooling

• Full Pooling : Combine everyone but you lose the details
• No Pooling: You don’t account for the other
• Partial pooling: You borrow

Use cases

References

1. Estimation of COVID-19 spread curves integrating global data and borrowing information
2. https://www.databricks.com/blog/2021/06/29/using-bayesian-hierarchical-models-to-infer-the-disease-parameters-of-covid-19.html