Fast Bayesian inference of Block Nearest Neighbor Gaussian models for large data

Zaida C. Quiroz, Marcos O. Prates, Dipak K. Dey, Haavard Rue

    Research output: Contribution to journalArticlepeer-review


    This paper presents the development of a spatial block-Nearest Neighbor Gaussian process (blockNNGP) for location-referenced large spatial data. The key idea behind this approach is to divide the spatial domain into several blocks which are dependent under some constraints. The cross-blocks capture the large-scale spatial dependence, while each block captures the smallscale spatial dependence. The resulting blockNNGP enjoys Markov properties reflected on its sparse precision matrix. It is embedded as a prior within the class of latent Gaussian models, thus fast Bayesian inference is obtained using the integrated nested Laplace approximation (INLA). The performance of the blockNNGP is illustrated on simulated examples, a comparison of our approach with other methods for analyzing large spatial data and applications with Gaussian and non-Gaussian real data.
    Original languageEnglish (US)
    JournalAccepted by Statistics and Computing
    StatePublished - Feb 21 2023

    Bibliographical note

    KAUST Repository Item: Exported on 2023-02-22
    Acknowledgements: The author would like to thank the referee for the suggestions that we believe drastically improved the context of the paper. Also, Zaida C. Quiroz would like to thank the Pontificia Universidad Cat´olica del Per´u for partial financial support through the project [DGI-2019-740]. Marcos O. Prates would like to acknowledge partial funding support from Conselho Nacional de Desenvolvimento Cient´ıfico e Tecnol´ogico (CNPq) grants 436948/2018-4 and 307547/2018-4 and Funda¸c˜ao de Amparo `a Pesquisa do Estado de Minas Gerais (FAPEMIG) grant APQ-01837-22.


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