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