25.7 Multivariate Student-t distribution, Cholesky parameterization
25.7.1 Probability density function
Let K∈N, ν∈R+, μ∈RK, and L a K×K lower-triangular matrix with strictly positive, finite diagonal then MultiStudentTCholesky(y∣ν,μ,L)=1πK/2 1νK/2 Γ((ν+K)/2)Γ(ν/2) 1|L| (1+1ν(y−μ)⊤L−TL−1(y−μ))−(ν+K)/2.
25.7.2 Sampling statement
y ~
multi_student_t_cholesky
(nu, mu, L)
Increment target log probability density with multi_student_t_cholesky_lupdf(y | nu, mu, L)
.
Available since 2.30
25.7.3 Stan functions
real
multi_student_t_cholesky_lpdf
(vectors y | real nu, vectors mu, matrix L)
The log of the multivariate Student-t density of vector or array of
vectors y
given
degrees of freedom nu
, location vector or array of vectors mu
, and Cholesky factor of the scale matrix L
.
For a definition of the arguments compatible with the vectors
type,
see the probability vectorization section.
Available since 2.30
real
multi_student_t_cholesky_lupdf
(vectors y | real nu, vectors mu, matrix L)
The log of the multivariate Student-t density of vector or vector
array y
given
degrees of freedom nu
, location vector or vector array mu
, and Cholesky factor of the scale matrix L
,
dropping constant additive terms. For a definition of arguments
compatible with the vectors
type, see the probability vectorization
section.
Available since 2.30
vector
multi_student_t_cholesky_rng
(real nu, vector mu, matrix L)
Generate a multivariate Student-t variate with degrees of freedom
nu
, location mu
, and Cholesky factor of the scale matrix L
; may only be used in transformed data
and generated quantities blocks.
Available since 2.30
array[] vector
multi_student_t_cholesky_rng
(real nu, array[] vector mu, matrix L)
Generate a multivariate Student-t variate with degrees of freedom
nu
, location array mu
, and Cholesky factor of the scale matrix L
; may only be used in transformed data
and generated quantities blocks.
Available since 2.30
array[] vector
multi_student_t_cholesky_rng
(real nu, array[] row_vector mu, matrix L)
Generate an array of multivariate Student-t variate with degrees of freedom
nu
, location array mu
, and Cholesky factor of the scale matrix L
; may only be used in transformed data
and generated quantities blocks.
Available since 2.30