LKJ.jl

A Julia package implementing the Lewandowski, Kurowicka and Joe (LKJ) probability distribution on the space of correlation matrices.

The probability density function of a d-dimensional LKJ-distribution (''d \geq 2'') with parameter ''\boldsymbol{\eta} \geq 1'' is:

$$f(\\mathbf{A}; \\boldsymbol{\\eta}) = c_d |det(A)|^{\\eta-1}$$

where ''\mathbf{A}'' is ''d \times d'' correlation matrix and ''c_d'' is a normalization constant depending on the dimension 'd'.

References

Lewandowski, Kurowicka, Joe (2009): Generating random correlation matrices based on vines and extended onion method. Journal of Multivariate Analysis. (DOI 10.1016/j.jmva.2009.04.008)