LKJ prior distribution

[Jenny]

why? I just connect the physical relationship to the parameter. From example, in river, the diffusion coefficient could not be larger than 1.0. So I assign the sigma has a range… Do you think is it reasonable?

[bgoodri]

1.0 is sometimes a theoretical upper bound or the limit for a process to stay in equilibrium; 0.89 less so.

[Trung_Dung_Tran]

Hi @bgoodri,

Thank you for a very interesting discussion!

Could you suggest me a reference for this so that I can include in my paper?

@bgoodri

The LKJ distribution for correlation matrices is basically a generalization of the beta distribution for scalars. By definition, a correlation is between -1 and 1 so the density of the LKJ distribution can be evaluated for any correlation matrix (that is positive definite). There is no generic way in Stan to construct a correlation matrix where the correlations are restricted to a subinterval of the (−1,1)(-1,1) interval.

A LKJ(10) differs from a LKJ(5) in much the same way a beta(10, 10) differs from a beta(5,5), in the sense that a beta(5,5) has less concentration at its mode. In the case of a correlation matrix, the mode is the identity matrix.

[bgoodri]

@article{lewandowski2009generating,
title={Generating random correlation matrices based on vines and extended onion method},
author={Lewandowski, Daniel and Kurowicka, Dorota and Joe, Harry},
journal={Journal of multivariate analysis},
volume={100},
number={9},
pages={1989–2001},
year={2009},
publisher={Elsevier}
}

[Trung_Dung_Tran]

Thank you so much!