multi_gp_cholesky_lpdf() [1/2]

template<bool propto, typename T_y , typename T_covar , typename T_w , require_all_eigen_matrix_dynamic_t< T_y, T_covar > * = nullptr, require_eigen_col_vector_t< T_w > * = nullptr>

return_type_t< T_y, T_covar, T_w > stan::math::multi_gp_cholesky_lpdf	(	const T_y &	y,
		const T_covar &	L,
		const T_w &	w
	)

The log of a multivariate Gaussian Process for the given y, w, and a Cholesky factor L of the kernel matrix Sigma.

Sigma = LL', a square, semi-positive definite matrix. y is a dxN matrix, where each column is a different observation and each row is a different output dimension. The Gaussian Process is assumed to have a scaled kernel matrix with a different scale for each output dimension. This distribution is equivalent to: for (i in 1:d) row(y, i) ~ multi_normal(0, (1/w[i])*LL').

Template Parameters

T_y	type of scalar
T_covar	type of kernel
T_w	type of weight

Parameters

y	A dxN matrix
L	The Cholesky decomposition of a kernel matrix
w	A d-dimensional vector of positive inverse scale parameters for each output.

Returns

The log of the multivariate GP density.

Exceptions

std::domain_error

if Sigma is not square, not symmetric, or not semi-positive definite.

Definition at line 41 of file multi_gp_cholesky_lpdf.hpp.