The Chinese Restaurant Process Distribution
Density and random generation for the Chinese Restaurant Process distribution.
dCRP(x, conc = 1, size, log = 0) rCRP(n, conc = 1, size)
x |
vector of values. |
conc |
scalar concentration parameter. |
size |
integer-valued length of |
log |
logical; if TRUE, probability density is returned on the log scale. |
n |
number of observations (only n = 1 is handled currently). |
The Chinese restaurant process distribution is a distribution
on the space of partitions of the positive integers.
The distribution with concentration parameter α equal to conc
has probability function
f(x_i \mid x_1, …, x_{i-1})=\frac{1}{i-1+α}∑_{j=1}^{i-1}δ_{x_j}+ \frac{α}{i-1+α}δ_{x^{new}},
where x^{new} is a new integer not in x_1, …, x_{i-1}.
If conc is not specified, it assumes the default value of 1. The conc
parameter has to be larger than zero. Otherwise, NaN are returned.
dCRP gives the density, and rCRP gives random generation.
Claudia Wehrhahn
Blackwell, D., and MacQueen, J. B. (1973). Ferguson distributions via P\'olya urn schemes. The Annals of Statistics, 1: 353-355.
Aldous, D. J. (1985). Exchangeability and related topics. In \'Ecole d'\'Et\'e de Probabilit\'es de Saint-Flour XIII - 1983 (pp. 1-198). Springer, Berlin, Heidelberg.
Pitman, J. (1996). Some developments of the Blackwell-MacQueen urn scheme. IMS Lecture Notes-Monograph Series, 30: 245-267.
x <- rCRP(n=1, conc = 1, size=10) dCRP(x, conc = 1, size=10)
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