BBRecapture (version 0.2)

rissanen: Rissanen's universal prior for integers

Description

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

Usage

rissanen(n)

Arguments

n

a vector of positive integers

Value

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 $$c = \sum_{n=1}^\infty Q(n)$$

Details

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 \(1/N^2\)

References

Rissanen, J. (1983) A universal prior for integers and estimation by minimum description length. Ann. Statist. 11, no. 2, 416-431

Examples

# NOT RUN {
# Notice that masses are not normalized hence they do not add to one,
# but to a finite positive real constant c

rissanen(1:5)

# }