Log-Gaussian Cox Process Modeling of Large Spatial Lightning Data using Spectral and Laplace Approximations

TL;DR

This paper introduces SLEM, a new computational method combining spectral and Laplace approximations within an EM algorithm, enabling efficient and accurate modeling of large-scale lightning spatial data using log-Gaussian Cox processes.

Contribution

The paper develops SLEM, a novel approach that improves computational feasibility and prediction accuracy for large spatial point pattern data, specifically applied to lightning datasets.

Findings

SLEM achieves competitive speed and accuracy in simulations.

SLEM outperforms existing methods in out-of-sample prediction.

SLEM provides faster runtimes for large lightning datasets.

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.