## Construction of the Hessian

The construction of the Hessian for the models , , , and is very similar to the procedure used for the gradient. The chi-squared Hessian for the global models and is

 ∇2χ2 = ∇2χ2i. (15.12)

Figure 15.2 demonstrates the construction of the full Hessian for the model . The Hessian for the model is the sum of all the red blocks. The Hessian for the model is the combination of the single red block for residue i, the two orange blocks representing the sub-matrices of chi-squared second partial derivatives with respect to the diffusion parameter and the model-free parameter , and the single yellow block for that residue. The Hessian for the model-free model is simply the sub-matrix for the residue i coloured yellow.

The relax user manual (PDF), created 2019-03-08.