#ML
The Bayesian hierarchical model provides a process to use Bayesian inference hierarchically to update the posteriors.
What is a Bayesian model? In a Bayesian linear regression problem, we can take the posterior from the previous data points and use it as our new prior for inferring based on new data. In other words, as more data coming in, our belief is being updated.
However, this is a problem if some clusters in the dataset have small sample sizes, aka small support. As we take these samples and fit them onto the model, we may get a huge credible interval.
One simple idea to mitigate this problem is to introduce some constraints on how the priors can change. For example, we can introduce a hyperprior that is parametrized by new parameters. Then the model becomes hierarchical since we will also have to model the new parameters.
The referenced post, "Bayesian Hierarchical Modeling at Scale", provides some examples of coding such models using numpyro with performance in mind.
https://florianwilhelm.info/2020/10/bayesian_hierarchical_modelling_at_scale/
The Bayesian hierarchical model provides a process to use Bayesian inference hierarchically to update the posteriors.
What is a Bayesian model? In a Bayesian linear regression problem, we can take the posterior from the previous data points and use it as our new prior for inferring based on new data. In other words, as more data coming in, our belief is being updated.
However, this is a problem if some clusters in the dataset have small sample sizes, aka small support. As we take these samples and fit them onto the model, we may get a huge credible interval.
One simple idea to mitigate this problem is to introduce some constraints on how the priors can change. For example, we can introduce a hyperprior that is parametrized by new parameters. Then the model becomes hierarchical since we will also have to model the new parameters.
The referenced post, "Bayesian Hierarchical Modeling at Scale", provides some examples of coding such models using numpyro with performance in mind.
https://florianwilhelm.info/2020/10/bayesian_hierarchical_modelling_at_scale/
