Nonparametric Bayesian statistics | Stochastic processes

Chinese restaurant 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 (i.e., they are more likely to sit at a table with many customers than few), or an unoccupied table. At time n, the n customers have been partitioned among m ≤ n tables (or blocks of the partition). 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. David J. Aldous attributes the restaurant analogy to and Lester Dubins in his 1983 book. (Wikipedia).

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Preferential attachment | Stochastic process | Pólya urn model | Exchangeable random variables | Hilbert's paradox of the Grand Hotel | Dirichlet process | Bayesian statistics | Digamma function | Pitman–Yor process | Gamma function | Partition of a set | Probability distribution | Probability measure | Stirling numbers of the first kind | Indian buffet process | Lester Dubins | Probability theory | Bernoulli distribution | Pochhammer k-symbol