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A synthetic likelihood approach for intractable markov random fields

Author

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  • Wanchuang Zhu

    (The University of Sydney
    The University of Sydney)

  • Yanan Fan

    (University of New South Wales
    University of New South Wales)

Abstract

We propose a new scalable method to approximate the intractable likelihood of the Potts model. The method decomposes the original likelihood into products of many low-dimensional conditional terms, and a Monte Carlo method is then proposed to approximate each of the small terms using their corresponding (exact) Multinomial distribution. The resulting tractable synthetic likelihood then serves as an approximation to the true likelihood. The method is scalable with respect to lattice size and can also be used for problems with irregular lattices. We provide theoretical justifications for our approach, and carry out extensive simulation studies, which show that our method performs at least as well as existing methods, whilst providing significant computational savings, up to ten times faster than the current fastest method. Finally, we include three real data applications for illustration.

Suggested Citation

  • Wanchuang Zhu & Yanan Fan, 2023. "A synthetic likelihood approach for intractable markov random fields," Computational Statistics, Springer, vol. 38(2), pages 749-777, June.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:2:d:10.1007_s00180-022-01256-x
    DOI: 10.1007/s00180-022-01256-x
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    References listed on IDEAS

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