In probability theory, the Chinese restaurant process is a discrete-time stochastic process, whose value at any positive-integer time n is a partition Bn of the set {1, 2, 3, ..., n} whose probability distribution is determined as follows. At time n = 1, the trivial partition { {1} } is obtained with probability 1. At time n + 1 the element n + 1 is either:
- added to one of the blocks of the partition Bn, where each block is chosen with probability |b|/(n + 1) where |b| is the size of the block, or
- added to the partition Bn as a new singleton block, with probability 1/(n + 1).
The random partition so generated is exchangeable in the sense that relabeling {1, ..., n} does not change the distribution of the partition, and it is consistent in the sense that the law of the partition of n − 1 obtained by removing the element n from the random partition at time n is the same as the law of the random partition at time n − 1.
Read more about Chinese Restaurant Process: Definition, Generalization, Applications
Famous quotes containing the words restaurant and/or process:
“In a restaurant one is both observed and unobserved. Joy and sorrow can be displayed and observed “unwittingly,” the writer scowling naively and the diners wondering, What the hell is he doing?”
—David Mamet (b. 1947)
“A process in the weather of the world
Turns ghost to ghost; each mothered child
Sits in their double shade.
A process blows the moon into the sun,
Pulls down the shabby curtains of the skin;
And the heart gives up its dead.”
—Dylan Thomas (1914–1953)