We introduce a new procedure for handling constraints in large intrinsic Gaussian Markov Random Fields. We propose the Hybrid Prior Precision Matrix Correction and Kriging method, dividing constraints into two separate sets where one part is enforced by correcting the precision matrix of the prior while the other one is approached by the standard conditioning by Kriging method. The prior correction introduces an approximation needed for numerical computation. A tuning parameter controls the amount of approximation error, and the error can be made small by making the tuning parameter large. The error can be made theoretically arbitrarily small. In practice though, the tuning parameter needs to take a large finite value.
The method is applicable to any intrinsic method. However, we focus on spatio-temporal models within the Knorr Held Type IV model class for the interaction terms, in which case we specify explicitly how the constraints can be divided into the prior-adjusted and posterior corrected parts. We demonstrate how the new method can easily be incorporated into INLA. Through experiments, we show that the new method produced essentially identical results compared to the standard conditioning by Kriging approach approach, but improves significantly on running time. This is also true when comparing with other competing methods.
This is joint work with Fredrik Lohne Aanes