# LKJ in stan function reference

**URL:** <https://discourse.mc-stan.org/t/lkj-in-stan-function-reference/14847>\
**Category:** General\
**Created:** [May 4, 2020, 8:27pm UTC](https://discourse.mc-stan.org/t/lkj-in-stan-function-reference/14847 "2020-05-04T20:27:25Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![jbaranowski](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jbaranowski/32/5734_2.png) [@jbaranowski](https://discourse.mc-stan.org/u/jbaranowski)\
**Post date:** [May 4, 2020, 8:27pm UTC](https://discourse.mc-stan.org/t/lkj-in-stan-function-reference/14847/1 "2020-05-04T20:27:26Z")

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In stan function reference [LKJ Cholesky](https://mc-stan.org/docs/2_23/functions-reference/cholesky-lkj-correlation-distribution.html) 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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**Author:** ![maxbiostat](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/maxbiostat/32/1326_2.png) [@maxbiostat](https://discourse.mc-stan.org/u/maxbiostat)\
**Post date:** [May 4, 2020, 8:50pm UTC](https://discourse.mc-stan.org/t/lkj-in-stan-function-reference/14847/2 "2020-05-04T20:50:22Z")

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@bgoodri is one of the people to ask.

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**Author:** ![bgoodri](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/bgoodri/32/4451_2.png) [@bgoodri](https://discourse.mc-stan.org/u/bgoodri)\
**Post date:** [May 4, 2020, 9:08pm UTC](https://discourse.mc-stan.org/t/lkj-in-stan-function-reference/14847/3 "2020-05-04T21:08:05Z")

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\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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**Author:** ![jbaranowski](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jbaranowski/32/5734_2.png) [@jbaranowski](https://discourse.mc-stan.org/u/jbaranowski)\
**Post date:** [May 4, 2020, 9:52pm UTC](https://discourse.mc-stan.org/t/lkj-in-stan-function-reference/14847/4 "2020-05-04T21:52:57Z")

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Could you point me to the explicit form of Jacobian?

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<div class="post-metadata">

**Author:** ![bgoodri](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/bgoodri/32/4451_2.png) [@bgoodri](https://discourse.mc-stan.org/u/bgoodri)\
**Post date:** [May 4, 2020, 10:15pm UTC](https://discourse.mc-stan.org/t/lkj-in-stan-function-reference/14847/5 "2020-05-04T22:15:33Z")

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> **[Stan Reference Manual](https://mc-stan.org/docs/2_23/reference-manual/cholesky-factors-of-correlation-matrices-1.html)**
>
> Stan reference manual specifying the syntax and semantics of the Stan programming language.