rissanen {BBRecapture} | R Documentation |
It returns (up to normalizing constant) the mass assigned to each positive integer or a vector of integers by Rissanen's universal prior for positive integers
rissanen(n)
n |
a vector of positive integers |
Rissanen's universal prior on positive integers is one of the default options for eliciting a noninformative prior distribution on the unknown population size N. It is a proper prior with tails of the order between 1/N and 1/N^2
The mass assigned to each positive integer in the input vector of integers n
by Rissanen's universal prior for positive integers
Q(n)=2^{-\log^*(n)} \qquad n>0
where \log^*(x)= \log(x)+\log( \log (x)) + \log( \log (\log (x))).... where the sum involves only the non-negative terms. Notice that masses are not normalized hence they do not add to one, but to a finite positive real constant
c = ∑_{n=1}^∞ Q(n)
Danilo Alunni Fegatelli and Luca Tardella
Rissanen, J. (1983) A universal prior for integers and estimation by minimum description length. Ann. Statist. 11, no. 2, 416-431
# Notice that masses are not normalized hence they do not add to one, # but to a finite positive real constant c rissanen(1:5)