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22.2 Multivariate Normal Distribution, Precision Parameterization

22.2.1 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 \(y \in \mathbb{R}^K\), \[ \text{MultiNormalPrecision}(y|\mu,\Omega) = \text{MultiNormal}(y|\mu,\Omega^{-1}) \]

22.2.2 Sampling Statement

y ~ multi_normal_prec(mu, Omega)

Increment target log probability density with multi_normal_prec_lupdf(y | mu, Omega).

22.2.3 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_lupdf(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 dropping constant additive terms

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_lupdf(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 dropping constant additive terms

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_lupdf(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 dropping constant additive terms

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

real multi_normal_prec_lupdf(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 dropping constant additive terms