# Chinese Restaurant Process
__Parent__: [Stochastic Processes](../stochastic_processes.md)
The Chinese Restaurant Process (CRP) is a stochastic process for expressing distributions
over partitions of $$[N] := \{1, ..., N\}$$. Consequently, the CRP is frequently used in problems involving
clustering. The CRP is also known as Ewens sampling formula.
## Definition
### Definition as Distribution Over Partitions
The Chinese Restaurant Process (CRP; \cite{aldous_exchangeability_1985}) is a
one-parameter (concentration parameter $\alpha > 0$) stochastic process that defines
a discrete distribution over the partitions of a set. The CRP defines a conditional distribution for
the $t$th discrete variable $z_t$ given the preceding variables:
$$
\begin{equation}
P(z_t = k | z_{