LKJChol
Prior family over Cholesky factors of correlation matrices.
Parameters
| Argument | Symbol | Meaning | Default |
|---|---|---|---|
eta |
\(\eta\) | LKJ shape parameter (eta > 0) |
1.0 |
K |
\(K\) | Correlation dimension | -1 |
random_state |
- | RNG seed / generator | None |
Dimension Parameter
K must be provided with a valid positive dimension for runtime use.
\[
f(R;\eta) = C \times \lbrack \det{R} \rbrack^{\eta-1}
\\
\text{ }
\\
\text{ }
\\
C = 2^{\sum_{k=1}^{K-1} (2(\eta-1)+K-k)(K-k)} \times \prod_{k=1}^{K-1}\Bigg\lbrack \Beta\bigg(\eta + \frac{(K-k-1)}{2}, \eta + \frac{(K-k-1)}{2}\bigg)\Bigg\rbrack^{K-k}
\]
Region
\[
L \in \mathcal{L}_K =
\left\{
L \in \mathbb{R}^{K\times K} :
L \text{ is lower triangular},\quad
L_{ii} > 0,\quad
\sum_{j=1}^{i} L_{ij}^2 = 1
\right\}
\]