Hierarchical Bayesian Models are statistical models that use a multi-level structure to analyze data. They allow for the incorporation of different levels of variability, such as individual differences and group effects, by organizing parameters into a hierarchy. This approach helps in making more accurate predictions and understanding complex data relationships. In these models, prior distributions are assigned to parameters at different levels, which are then updated with observed data to produce posterior distributions. This process leverages the principles of Bayesian statistics, enabling researchers to incorporate prior knowledge and improve inference in various fields, including psychology, economics, and machine learning.