Abstract
Lightning is a destructive and highly visible product of severe storms, yet there is still much to be learned about the conditions under which lightning is most likely to occur. The GOES-16 and GOES-17 satellites, launched in 2016 and 2018 by NOAA and NASA, collect a wealth of data regarding individual lightning strike occurrence and potentially related atmospheric variables. The acute nature and inherent spatial correlation in lightning data renders standard regression analyses inappropriate. Further, computational considerations are foregrounded by the desire to analyze the immense and rapidly increasing volume of lightning data. We present a new computationally feasible method that combines spectral and Laplace approximations in an EM algorithm, denoted SLEM, to fit the widely popular log-Gaussian Cox process model to large spatial point pattern datasets. In simulations we find SLEM is competitive with contemporary techniques in terms of speed and accuracy. When applied to two lightning datasets, SLEM provides better out-of-sample prediction scores and quicker runtimes, suggesting its particular usefulness for analyzing lightning data which tend to have sparse signals.
Funding Statement
The authors gratefully acknowledge financial support from the National Science Foundation 1455172, 1916208, 1934985, 1940124, 1940276, 1953088, and 2114143, USAID 7200AA18CA00014, National Institutes of Health R01ES027892, and Cornell Atkinson Center for Sustainability.
Acknowledgments
The authors would like to thank Finn Lindgren and Matthias Katzfuss for their aid in implementing INLA and VL, respectively.
Citation
Megan L. Gelsinger. Maryclare Griffin. David Matteson. Joseph Guinness. "Log-Gaussian Cox process modeling of large spatial lightning data using spectral and Laplace approximations." Ann. Appl. Stat. 17 (3) 2078 - 2094, September 2023. https://doi.org/10.1214/22-AOAS1708
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