Bayesian Hierarchical Models

Bayesian hierarchical models are a way to analyze complex data by recognizing that information can be grouped at multiple levels. For example, in studying students across different schools, these models consider individual student data and also account for differences between schools. They use probability to update our beliefs based on observed data, incorporating both overall patterns and group-specific variations. This approach allows for more accurate, flexible inferences, especially when data is sparse or unevenly distributed, by sharing information across related groups while respecting their unique characteristics.