Lewandowski-Kurowicka-Joe (LKJ) distribution is a very useful prior distribution for parameter estimation in correlation matrices, and is also tightly related to matrix factorizations such as Cholesky decomposition. For example, when you use Cholesky decomposition to decompose a variance-covariance matrix (Sigma) into the multiplication of 3 matrices, you can set LKJCorr prior for the correlation matrix R.
