Bayesian hierarchical models can be used for a variety of purposes, including prediction and causal inference from experimental and observational studies. The benefits of Bayesian modeling include uncertainty quantification for all model parameters and predictions, as well as the ability to interpret the outcome. Unfortunately, Bayesian inference, the process of fitting such models to datasets, is hard to implement. Stan is the state-of-the-art, open-source Bayesian inference engine which makes Bayesian inference much easier to use. We illustrate this with an application of Bayesian modeling in the field of clinical research, assessing the safety of approving a drug for market. To do this, we use PyStan, the Python interface to Stan.
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