  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.
