25.4 Multivariate Gaussian process distribution
25.4.1 Probability density function
If K,N∈N, Σ∈RN×N is symmetric, positive definite kernel matrix and w∈RK is a vector of positive inverse scales, then for y∈RK×N, MultiGP(y|Σ,w)=K∏i=1MultiNormal(yi|0,w−1iΣ), where yi is the ith row of y. This is used to efficiently handle Gaussian Processes with multi-variate outputs where only the output dimensions share a kernel function but vary based on their scale. Note that this function does not take into account the mean prediction.
25.4.2 Sampling statement
y ~
multi_gp
(Sigma, w)
Increment target log probability density with multi_gp_lupdf(y | Sigma, w)
.
Available since 2.3
25.4.3 Stan functions
real
multi_gp_lpdf
(matrix y | matrix Sigma, vector w)
The log of the multivariate GP density of matrix y given kernel matrix
Sigma and inverses scales w
Available since 2.12
real
multi_gp_lupdf
(matrix y | matrix Sigma, vector w)
The log of the multivariate GP density of matrix y given kernel matrix
Sigma and inverses scales w dropping constant additive terms
Available since 2.25