This is an old version, view current version.

22.4 Multivariate Gaussian Process Distribution

22.4.1 Probability Density Function

If K,NN, ΣRN×N is symmetric, positive definite kernel matrix and wRK is a vector of positive inverse scales, then for yRK×N, MultiGP(y|Σ,w)=Ki=1MultiNormal(yi|0,w1iΣ), 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.

22.4.2 Sampling Statement

y ~ multi_gp(Sigma, w)

Increment target log probability density with multi_gp_lpdf( y | Sigma, w) dropping constant additive terms.

22.4.3 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