22.3 Multivariate Normal Distribution, Cholesky Parameterization
22.3.1 Probability Density Function
If K∈N, μ∈RK, and L∈RK×K is lower triangular and such that LL⊤ is positive definite, then for y∈RK, MultiNormalCholesky(y|μ,L)=MultiNormal(y|μ,LL⊤). If L is lower triangular and LLtop is a K×K positive definite matrix, then Lk,k must be strictly positive for k∈1:K. If an L is provided that is not the Cholesky factor of a positive-definite matrix, the probability functions will raise errors.
22.3.2 Sampling Statement
y ~
multi_normal_cholesky
(mu, L)
Increment target log probability density with multi_normal_cholesky_lpdf( y | mu, L)
dropping constant additive terms.
22.3.3 Stan Functions
real
multi_normal_cholesky_lpdf
(vectors y | vectors mu, matrix L)
The log of the multivariate normal density of vector(s) y given
location vector(s) mu and lower-triangular Cholesky factor of the
covariance matrix L
real
multi_normal_cholesky_lpdf
(vectors y | row_vectors mu, matrix L)
The log of the multivariate normal density of vector(s) y given
location row vector(s) mu and lower-triangular Cholesky factor of the
covariance matrix L
real
multi_normal_cholesky_lpdf
(row_vectors y | vectors mu, matrix L)
The log of the multivariate normal density of row vector(s) y given
location vector(s) mu and lower-triangular Cholesky factor of the
covariance matrix L
real
multi_normal_cholesky_lpdf
(row_vectors y | row_vectors mu, matrix L)
The log of the multivariate normal density of row vector(s) y given
location row vector(s) mu and lower-triangular Cholesky factor of the
covariance matrix L
vector
multi_normal_cholesky_rng
(vector mu, matrix L)
Generate a multivariate normal variate with location mu and
lower-triangular Cholesky factor of the covariance matrix L; may only
be used in generated quantities block
vector
multi_normal_cholesky_rng
(row_vector mu, matrix L)
Generate a multivariate normal variate with location mu and
lower-triangular Cholesky factor of the covariance matrix L; may only
be used in generated quantities block
vectors
multi_normal_cholesky_rng
(vectors mu, matrix L)
Generate an array of multivariate normal variates with locations mu
and lower-triangular Cholesky factor of the covariance matrix L; may
only be used in generated quantities block
vectors
multi_normal_cholesky_rng
(row_vectors mu, matrix L)
Generate an array of multivariate normal variates with locations mu
and lower-triangular Cholesky factor of the covariance matrix L; may
only be used in generated quantities block