It’s a copula model that does something a little like:
- Create covariance:
\begin{align}
L &\sim \text{LKJCholesky}(2), \; R \sim \text{LKJCorr}(2) \\
\sigma &\sim \text{InverseGamma}(\alpha, \beta) \\
\Sigma &\sim LL^{T} = diag(\sigma) * R * diag(\sigma)
\end{align}
- Transform actually observed marginals via their CDFs:
\begin{align}
\mathbf{m1u}_{y} &= \mathfrak{m1}_{y}\Phi(\mathbf{m1}_{y}) \\
\mathbf{m2u}_{y} &= \mathfrak{m2}_{y}\Phi(\mathbf{m2}_{y})
\end{align}
- Transform the now-uniform-transformed marginals via a Normal InvCDF:
\begin{align}
(\mathbf{m1n}, \mathbf{m2n})_{y} &= \text{MvNormal}(\mu=0, \sigma=1)\Phi^{-1}([\mathbf{m1u}_{y}, \mathbf{m2u}_{y}])
\end{align}
- Evaluate likelihood at the copula:
\begin{align}
copula &\sim \text{MvNormal}(\mu=0, \Sigma, observed=(\mathbf{m1n}, \mathbf{m2n})_{y}
\end{align}