A Marginalizing Gaussian Edge Weights If we set the prior over edge weights to be a d (d 1) /2-dimensional isotropic Gaussian with standard deviation ν, so l N (0, Σ l) with Σ l = Iν

The following theorem provides a closed-form expression for this integral. D has (almost surely) one zero diagonal entry, with index i. We can compute this analytically. We write l for the vector of d(d 1) / 2 strictly lower-triangular elements, and L for the matrix with these as the lower-triangular elements. Since L is the integration variable, the first term (not containing L) can be taken outside the integral.