  The Chinese restaurant process (CRP) and the stick-breaking process are the
two most commonly used representations of the Dirichlet process. However, the
usual proof of the connection between them is indirect, relying on abstract
properties of the Dirichlet process that are difficult for nonexperts to
verify. This short note provides a direct proof that the stick-breaking process
leads to the CRP, without using any measure theory. We also discuss how the
stick-breaking representation arises naturally from the CRP.
