Chinese restaurant process

Discrete-time stochastic process

In probability theory, the Chinese restaurant process is a discrete-time stochastic process, analogous to seating customers at tables in a restaurant. Imagine a restaurant with an infinite number of circular tables, each with infinite capacity. Customer 1 sits at the first table. The next customer either sits at the same table as customer 1, or the next table. This continues, with each customer choosing to either sit at an occupied table with a probability proportional to the number of customers already there, or an unoccupied table. At time n, the n customers have been partitioned among m ≤ n tables. The results of this process are exchangeable, meaning the order in which the customers sit does not affect the probability of the final distribution. This property greatly simplifies a number of problems in population genetics, linguistic analysis, and image recognition.

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