Gibbs Markov random fields with continuous values based on the modified planar rotator modelGibbs Markov random fields with continuous values based on the modified planar rotator model Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2019-05-212018enWe introduce a Gibbs Markov random field for spatial data on Cartesian grids based on the modified planar rotator (MPR) model of statistical physics. The MPR model captures spatial correlations using nearest-neighbor interactions of continuously valued spins and does not rely on Gaussian assumptions. The only model parameter is the reduced temperature, which we estimate by means of an ergodic specific energy matching principle. We propose an efficient hybrid Monte Carlo simulation algorithm that leads to fast relaxation of the MPR model and allows vectorization. Consequently, the MPR model's computational time for inference and simulation scales approximately linearly with system size. This makes it more suitable for big data sets, such as satellite and radar images, than conventional geostatistical approaches. The performance (accuracy and computational speed) of the MPR model is validated with conditional simulation of Gaussian synthetic and non-Gaussian real data (atmospheric heat release measurements and Walker-lake DEM-based concentrations) and comparisons with standard gap-filling methods. © 2018 American Physical Society.http://creativecommons.org/licenses/by/4.0/Physical Review E - Statistical, Nonlinear, and Soft Matter Physics986 Žukovič, Milan Christopoulos Dionysios Χριστοπουλος Διονυσιος American Physical Society Classical statistical mechanics Environmental research Stochastic inference Stochastic processes Classical spin models Equilibrium lattice models Lattice models in statistical physics Computational complexity Data analysis Hybrid Monte Carlo algorithm Markovian processes Metropolis algorithm Monte Carlo methods Spatial modeling Statistical methods Stochastic analysis XY model Gaussian distribution Image segmentation Intelligent systems Markov processes Statistical Physics