  The COVID-19 pandemic has led to a vast amount of growth for statistical
models and methods which characterize features of disease outbreaks. One class
of models that came to light in this regard has been the use of self-exciting
point processes, wherein infections occur both "at random" and also more
systematically from person-to-person transmission. Beyond the modeling of the
overall COVID-19 outbreak, the pandemic has also motivated research assessing
various policy decisions and event outcomes. One such area of study, addressed
here, relates to the formulation of methods which measure the impact that large
events or gatherings of people had in the local areas where the events were
held. We formulate an alternative approach to traditional causal inference
methods and then apply our method to assessing the impact that then President
Donald Trump's re-election campaign rallies had on COVID-19 infections in areas
where the rallies were hosted. By incorporating several adaptions to
nonparametric self-exciting point process models, we estimate both the excess
number of COVID-19 infections brought on by the rallies and the duration of
time in which these excess infections persisted.
