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25.4 Multivariate Gaussian process distribution

25.4.1 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.

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