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Spatially varying SAR models and Bayesian inference for high-resolution lattice data

  • Special Issue: Bayesian Inference and Stochastic Computation
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Abstract

We discuss a new class of spatially varying, simultaneous autoregressive (SVSAR) models motivated by interests in flexible, non-stationary spatial modelling scalable to higher dimensions. SVSAR models are hierarchical Markov random fields extending traditional SAR models. We develop Bayesian analysis using Markov chain Monte Carlo methods of SVSAR models, with extensions to spatio-temporal contexts to address problems of data assimilation in computer models. A motivating application in atmospheric science concerns global CO emissions where prediction from computer models is assessed and refined based on high-resolution global satellite imagery data. Application to synthetic and real CO data sets demonstrates the potential of SVSAR models in flexibly representing inhomogeneous spatial processes on lattices, and their ability to improve estimation and prediction of spatial fields. The SVSAR approach is computationally attractive in even very large problems; computational efficiencies are enabled by exploiting sparsity of high-dimensional precision matrices.

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Acknowledgments

We are grateful to the Editor and two anonymous referees for their positive and constructive comments on an earlier version of the paper, and to Abel Rodriguez for useful comments and suggestions. This work was partly supported by Grants from the US National Science Foundation [M.W., #DMS-1106516] and the US National Aeronautics and Space Administration [P.S.K., sub-award 2011-2654 of Grant #NNX11AF96G to the University of California at Irvine]. Any opinions, findings and conclusions or recommendations expressed in this work are those of the authors and do not necessarily reflect the views of the NSF or NASA.

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Authors and Affiliations

  1. Google Inc., Mountain View, CA, 94043, USA

    Chiranjit Mukherjee

  2. Nicholas School of the Environment, Duke University, Durham, NC, 27708, USA

    Prasad S. Kasibhatla

  3. Department of Statistical Science, Duke University, Durham, NC, 27708, USA

    Mike West

Authors
  1. Chiranjit Mukherjee
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  2. Prasad S. Kasibhatla
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  3. Mike West
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Correspondence to Mike West.

Additional information

This work was completed while C. Mukherjee was a PhD student in Statistical Science at Duke University.

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Mukherjee, C., Kasibhatla, P.S. & West, M. Spatially varying SAR models and Bayesian inference for high-resolution lattice data. Ann Inst Stat Math 66, 473–494 (2014). https://doi.org/10.1007/s10463-013-0426-9

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  • DOI: https://doi.org/10.1007/s10463-013-0426-9

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