Sometimes, data contain multiple entries from observation units. For example, researchers may be interested in effectiveness of medical treatments, and tested several treatments in several different cities. Then, it may make sense to consider that the effectiveness may be overall consistent across cities but slightly vary between the cities, as population characteristic may vary between the cities. For instance, one city may have more younger people than another. In these cases, hierarchical Bayes may help. In this blog post, I review hierarchical Bayes.

In cognitive science/psychology, Dirichlet process mixture model (DPMM) is considered as a rational model of category learning (Anderson, 1991; Sanborn, Griffiths & Navarro, 2010). That is, the DPMM is used to approximate how human learns to categorise objects.

In this post, I review the DPMM, assuming that all the features are discrete. The implementation in C++ can be found here.