Estimating a Centered Matérn (1) Process: Three Alternatives to Maximum Likelihood via Conjugate Gradient Linear Solvers
Résumé
http://demonstrations.wolfram.com/EstimatingACenteredMatern1ProcessThreeAlternativesToMaximumL/.
Estimating a Centered Matérn (1) Process: Three Alternatives to Maximum Likelihood via Conjugate Gradient Linear Solvers.
The setting is the same as in the Demonstration "Three Alternatives to the Likelihood Maximization for Estimating a Centered Matérn (3/2) Process", except that the "differentiability" parameter (often denoted by \[Nu]) is fixed here to 1 (classically used in two dimensions following the seminal work of Whittle) instead of 3/2. An important difference in the implementation of the fixed-point algorithm (for approximating the root of the GE-EV estimating equation) is that an iterative linear solver is used now (precisely a conjugate-gradient (CG) solver preconditioned by a classical factored sparse approximate inverse). It is observed here that this implementation is quite fast, even for a data size as large as 8196.