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Yet the classic causal inference framework is not directly applicable when the treatment and outcome variables are generated by spatio-temporal point processes. We extend the potential outcomes framework to these settings by formulating the treatment point process as a stochastic intervention. Our causal estimands include the expected number of outcome events in a specified area under a particular stochastic treatment assignment strategy. Our methodology allows for arbitrary patterns of spatial spillover and temporal carryover effects. Using martingale theory, we show that the proposed estimator is consistent and asymptotically normal as the number of time periods increases. We propose a sensitivity analysis for the possible existence of unmeasured confounders, and extend it to the H\u00e1jek estimator. Simulation studies are conducted to examine the estimators' finite sample performance. Finally, we illustrate the proposed methods by estimating the effects of American airstrikes on insurgent violence in Iraq from February 2007 to July 2008. Our analysis suggests that increasing the average number of daily airstrikes for up to 1 month may result in more insurgent attacks. We also find some evidence that airstrikes can displace attacks from Baghdad to new locations up to 400 km away.<\/jats:p>","DOI":"10.1111\/rssb.12548","type":"journal-article","created":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T11:15:30Z","timestamp":1669115730000},"page":"1969-1999","source":"Crossref","is-referenced-by-count":22,"title":["Causal Inference with Spatio-Temporal Data: Estimating the Effects of Airstrikes on Insurgent Violence in Iraq"],"prefix":"10.1093","volume":"84","author":[{"given":"Georgia","family":"Papadogeorgou","sequence":"first","affiliation":[{"name":"Department of Statistics , , Gainesville , Florida , USA"},{"name":"University of Florida , , Gainesville , Florida , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kosuke","family":"Imai","sequence":"additional","affiliation":[{"name":"Department of Government and Department of Statistics, Institute for Quantitative Social Science , , Cambridge , Massachusetts , USA"},{"name":"Harvard University , , Cambridge , Massachusetts , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jason","family":"Lyall","sequence":"additional","affiliation":[{"name":"Department of Government , , Hanover , New Hampshire , USA"},{"name":"Dartmouth College , , Hanover , New Hampshire , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fan","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Statistical Science , , Durham , North Carolina , USA"},{"name":"Duke University , , Durham , North Carolina , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2022,11,22]]},"reference":[{"issue":"4","key":"2023112203425166200_rssb12548-bib-0001","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1214\/aos\/1176345986","article-title":"On bandwidth variation in kernel estimates-a square root law","volume":"10","author":"Abramson","year":"1982","journal-title":"The Annals of Statistics"},{"key":"2023112203425166200_rssb12548-bib-0002","volume-title":"Design-based inference for spatial experiments with interference. 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