Bayesian Estimation for Homogeneous and Inhomogeneous Gaussian Random Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the underfitting and overfitting sets of models chosen by order selection criteria
Journal of Multivariate Analysis
Conditional-mean least-squares fitting of Gaussian Markov random fields to Gaussian fields
Computational Statistics & Data Analysis
A comparative study of Gaussian geostatistical models and Gaussian Markov random field models
Journal of Multivariate Analysis
Data-driven Calibration of Penalties for Least-Squares Regression
The Journal of Machine Learning Research
Wavelet-based statistical signal processing using hidden Markovmodels
IEEE Transactions on Signal Processing
Valid parameter space of 2-D Gaussian Markov random fields
IEEE Transactions on Information Theory
Image denoising using scale mixtures of Gaussians in the wavelet domain
IEEE Transactions on Image Processing
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The nonparametric covariance estimation of a stationary Gaussian field X observed on a lattice is investigated. To tackle this issue, a neighborhood selection procedure has been recently introduced. This procedure amounts to selecting a neighborhood m@^ by a penalization method and estimating the covariance of X in the space of Gaussian Markov random fields (GMRFs) with neighborhood m@^. Such a strategy is shown to satisfy oracle inequalities as well as minimax adaptive properties. However, it suffers several drawbacks which make the method difficult to apply in practice: the penalty depends on some unknown quantities and the procedure is only defined for toroidal lattices. The contribution is threefold. Firstly, a data-driven algorithm is proposed for tuning the penalty function. Secondly, the procedure is extended to non-toroidal lattices. Thirdly, numerical study illustrates the performances of the method on simulated examples. These simulations suggest that Gaussian Markov random field selection is often a good alternative to variogram estimation.