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Keywords:

  • Block sampling;
  • Conditional autoregressive model;
  • Divide-and-conquer strategy;
  • Gaussian Markov random field;
  • Markov chain Monte Carlo methods

This paper demonstrates how Gaussian Markov random fields (conditional autoregressions) can be sampled quickly by using numerical techniques for sparse matrices. The algorithm is general and efficient, and expands easily to various forms for conditional simulation and evaluation of normalization constants. We demonstrate its use by constructing efficient block updates in Markov chain Monte Carlo algorithms for disease mapping.