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Performing a Bayesian inference on large spatio-temporal models requiresextracting inverse elements of large sparse precision matrices for marginalvariances. Although direct matrix factorizations can be used for the inversion,such methods fail to scale well for distributed problems when run on largecomputing clusters. On the contrary, Krylov subspace methods for the selectedinversion have been gaining traction. We propose a parallel hybrid approachbased on domain decomposition, which extends the Rao-Blackwellized Monte Carloestimator for distributed precision matrices. Our approach exploits thestrength of Krylov subspace methods as global solvers and efficiency of directfactorizations as base case solvers to compute the marginal variances using adivide-and-conquer strategy. By introducing subdomain overlaps, one can achievea greater accuracy at an increased computational effort with little to noadditional communication. We demonstrate the speed improvements on bothsimulated models and a massive US daily temperature data.

Parallel Selected Inversion for Space-Time Gaussian Markov Random Fields