# Using LKJ priors

**URL:** <https://discourse.pymc.io/t/using-lkj-priors/6233>\
**Category:** Questions\
**Created:** [November 9, 2020, 10:22am UTC](https://discourse.pymc.io/t/using-lkj-priors/6233 "2020-11-09T10:22:14Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![guro86](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/guro86/32/3313_2.png) [@guro86](https://discourse.pymc.io/u/guro86)\
**Post date:** [November 9, 2020, 10:22am UTC](https://discourse.pymc.io/t/using-lkj-priors/6233/1 "2020-11-09T10:22:14Z")

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I have a problem where I want to apply the method referred to as “margin” in Pernot, Pascal, and Fabien Cailliez. “A Critical Review of Statistical Calibration/Prediction Models Handling Data Inconsistency and Model Inadequacy.” _AIChE Journal_ , 2016 to solve for model inadequacy.

For the Cholesky component L of the covariance matrix, Vm, I’m using the LKJCholeskyCov, which seems to work well for a 2x2 matrix Vm. What I quite don’t understand, is that in the implementation of LKJCholeskyCov, there is a determinant of the jacobian of the transformation referred to as ϕ−1. Why is that needed?

Will it bee the same thing to use a separate LK prior on the correlation matrix wich pdf© proportional to |C| ^ (eta -1), whatever needed for the standard deviation vector, and then construct Vm as:

Vm = diag(sd) @ C @ diag(sd)

Probably not? I would appreciate it if someone could explain this.

Thanks,

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**Author:** ![guro86](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/guro86/32/3313_2.png) [@guro86](https://discourse.pymc.io/u/guro86)\
**Post date:** [November 18, 2020, 10:09am UTC](https://discourse.pymc.io/t/using-lkj-priors/6233/2 "2020-11-18T10:09:19Z")

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No one that can provide some feedback on this?

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**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [November 18, 2020, 12:59pm UTC](https://discourse.pymc.io/t/using-lkj-priors/6233/3 "2020-11-18T12:59:40Z")

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@aseyboldt

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**Author:** ![guro86](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/guro86/32/3313_2.png) [@guro86](https://discourse.pymc.io/u/guro86)\
**Post date:** [December 14, 2020, 1:36pm UTC](https://discourse.pymc.io/t/using-lkj-priors/6233/4 "2020-12-14T13:36:19Z")

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Hello, I’d really like someone’s inputs on this, so I’m kindly asking again. Maybe I have to clarify the question if you believe you know this, please write to me if the question needs clarification.