here <span class="math inline">\(y_i\)</span> is the <span class="math inline">\(i\)</span>th row of <span class="math inline">\(y\)</span>. 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. If the model allows parameterization in terms of Cholesky factor of the kernel matrix, this distribution is also more efficient than <span class="math inline">\(\text{MultiGP}()\)</span>. Note that this