Sampling from Gaussian Markov random fields conditioned on linear constraints

Daniel Peter Simpson, Ian W. Turner, A. N. Pettitt


Gaussian Markov random fields (GMRFs) are important modeling tools in statistics. They are often utilised to model spatially structured uncertainty, seasonal variation and other trends in the data. These last two examples of GMRFs are part of a larger class of GMRFs conditioned on linear constraints. Performing Monte Carlo Markov Chain inference on these models requires a large number of samples from GMRFs conditioned on linear constraints. Therefore it is vital to have fast and efficient methods for performing these samples. This article presents three Krylov subspace methods for sampling from a GMRF conditioned on linear constraints based on solving a Karush--Kuhn--Tucker, or saddle point, system.

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