LKJ in stan function reference

General
1

In stan function reference LKJ Cholesky is described in the following form:

\mathrm{LkjCholesky}(L|\eta)\propto |J|\mathrm{det}(LL^\mathsf{T})^{\eta-1}=\prod_{k=2}^KL_{kk}^{K-k+2\eta-2}

However I cannot find the explanation what is J. Can someone help?

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2

@bgoodri is one of the people to ask.

3

\mathbf{J} is the Jacobian matrix of the transformation from the Cholesky factor, \mathbf{L}, to the correlation matrix \mathbf{L}\mathbf{L}^\top.

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Could you point me to the explicit form of Jacobian?

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