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.

翻译：COVID-19大流行已导致统计模式和方法的巨大增长,这些模式是疾病爆发特点的特点。在这方面,发现的一种模式是使用自我激发的点过程,即感染“随机”和更系统地从人与人之间传染。除了对COVID-19大爆发进行模拟外,该流行病还激发了各种研究,评估各种政策决定和事件结果。这里讨论的这类研究领域之一是制定方法,衡量大型事件或人们集会在事件发生地的当地地区产生的影响。我们制定了传统因果推断方法的替代方法,然后运用我们的方法评估当时的唐纳德·特朗普总统的重新竞选集会在举行集会的地区对COVID-19感染的影响。通过将若干调整纳入非参数性自我激发点进程模型,我们估计了集会带来的COVID-19感染过多的数量和这些超重感染持续的时间。