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## 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