Gaussian Markov random fields and Donald Duck

Gaussian Markov random fields (GMRF) are a powerful tool for making a priori distributions for Bayesian inversion. By suitable parameterisation via latent variables, we can describe a big number of features, for example ionospheric structures. In order to demonstrate the flexibility of  GMRFs, below is the Random Duck demonstration done by drawing random samples of a certain GMRF with varying correlation structure.

For more details on Gaussian Markov random fields, see for example correlation priors paper (Roininen et al. 2011).