21.2 Multivariate Normal Distribution, Precision Parameterization
21.2.1 Probability Density Function
If \(K \in \mathbb{N}\), \(\mu \in \mathbb{R}^K\), and \(\Omega \in \mathbb{R}^{K \times K}\) is symmetric and positive definite, then for \(y \in \mathbb{R}^K\), \[ \text{MultiNormalPrecision}(y|\mu,\Omega) = \text{MultiNormal}(y|\mu,\Omega^{-1}) \]
21.2.2 Sampling Statement
y ~ multi_normal_prec(mu, Omega)
Increment target log probability density with multi_normal_prec_lpdf(y | mu, Omega) dropping constant additive terms.
21.2.3 Stan Functions
real multi_normal_prec_lpdf(vectors y | vectors mu, matrix Omega)
The log of the multivariate normal density of vector(s) y given location vector(s) mu and positive definite precision matrix Omega
real multi_normal_prec_lpdf(vectors y | row_vectors mu, matrix Omega)
The log of the multivariate normal density of vector(s) y given location row vector(s) mu and positive definite precision matrix Omega
real multi_normal_prec_lpdf(row_vectors y | vectors mu, matrix Omega)
The log of the multivariate normal density of row vector(s) y given location vector(s) mu and positive definite precision matrix Omega
real multi_normal_prec_lpdf(row_vectors y | row_vectors mu, matrix Omega)
The log of the multivariate normal density of row vector(s) y given location row vector(s) mu and positive definite precision matrix Omega