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25.7 Multivariate Student-t distribution, Cholesky parameterization

25.7.1 Probability density function

Let KN, νR+, μRK, and L a K×K lower-triangular matrix with strictly positive, finite diagonal then MultiStudentTCholesky(yν,μ,L)=1πK/2 1νK/2 Γ((ν+K)/2)Γ(ν/2) 1|L| (1+1ν(yμ)LTL1(yμ))(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