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Bayesian Hierarchical Models for the Combination of Spatially Misaligned Data: A Comparison of Melding and Downscaler Approaches Using INLA and SPDE

Author

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  • Ruiman Zhong

    (King Abdullah University of Science and Technology (KAUST))

  • Paula Moraga

    (King Abdullah University of Science and Technology (KAUST))

Abstract

The spatially misaligned data problem occurs when data at different spatial scales need to be combined. Bayesian hierarchical models such as melding and downscaler approaches are suitable to solve this problem but their application is limited when MCMC is used for inference due to the high computational cost. The use of INLA and SPDE represents an alternative to MCMC for Bayesian inference that enables faster inference for latent Gaussian models. In this paper, we describe how INLA and SPDE can be adapted to fit Bayesian melding and downscaler models to combine spatially misaligned data. We assess the performance of the models using simulated and real data in a range of scenarios and sampling strategies and compare the suitability of the models in each situation. We also show how to obtain fine particulate matter (PM $$_{2.5}$$ 2.5 ) predictions in the UK at a continuous surface and at policy-relevant spatial scales by combining spatially misaligned monitoring station data, satellite-derived indicators, road information, and environmental factors.

Suggested Citation

  • Ruiman Zhong & Paula Moraga, 2024. "Bayesian Hierarchical Models for the Combination of Spatially Misaligned Data: A Comparison of Melding and Downscaler Approaches Using INLA and SPDE," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(1), pages 110-129, March.
    • Handle: RePEc:spr:jagbes:v:29:y:2024:i:1:d:10.1007_s13253-023-00559-w
    DOI: 10.1007/s13253-023-00559-w
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    References listed on IDEAS

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    1. Michela Cameletti & Finn Lindgren & Daniel Simpson & Håvard Rue, 2013. "Spatio-temporal modeling of particulate matter concentration through the SPDE approach," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(2), pages 109-131, April.
    2. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    3. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
    4. Lindgren, Finn & Rue, Håvard, 2015. "Bayesian Spatial Modelling with R-INLA," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i19).
    5. Montserrat Fuentes & Adrian E. Raftery, 2005. "Model Evaluation and Spatial Interpolation by Bayesian Combination of Observations with Outputs from Numerical Models," Biometrics, The International Biometric Society, vol. 61(1), pages 36-45, March.
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