  The Hawkes process and its extensions effectively model self-excitatory
phenomena including earthquakes, viral pandemics, financial transactions,
neural spike trains and the spread of memes through social networks. The
usefulness of these stochastic process models within a host of economic sectors
and scientific disciplines is undercut by the processes' computational burden:
complexity of likelihood evaluations grows quadratically in the number of
observations for both the temporal and spatiotemporal Hawkes processes. We show
that, with care, one may parallelize these calculations using both central and
graphics processing unit implementations to achieve over 100-fold speedups over
single-core processing. Using a simple adaptive Metropolis-Hastings scheme, we
apply our high-performance computing framework to a Bayesian analysis of big
gunshot data generated in Washington D.C. between the years of 2006 and 2019,
thereby extending a past analysis of the same data from under 10,000 to over
85,000 observations. To encourage wide-spread use, we provide hpHawkes, an
open-source R package, and discuss high-level implementation and program design
for leveraging aspects of computational hardware that become necessary in a big
data setting.
