Log exchangeable partition probability function of a Pitman-Yor process

Evaluates the log EPPF \(\log\{\prod_{j=1}^{k-1} (\theta + j d) / (\theta + 1)_{n-1} \prod_j (1 - d)_{n_j - 1}\}\) for a partition of \(n = \sum_j n_j\) items into \(k\) blocks of the given sizes. The blocks are exchangeable, so only the multiset of sizes matters.

Usage

morie_gh_py_eppf_log(sizes, d, theta)

Arguments

sizes

numeric vector of block sizes of the partition

d

discount parameter, typically in \([0, 1)\)

theta

concentration parameter, typically \(> -d\)

Value

numeric scalar log-probability of the partition

References

Ghosal, S. and van der Vaart, A. (2017). Fundamentals of Nonparametric Bayesian Inference. Cambridge University Press.

Examples

morie_gh_py_eppf_log(sizes = c(3, 2, 1), d = 0.25, theta = 1)
#> [1] -5.966391