Hate speech is ubiquitous on the Web. Recently, the offline causes that contribute to online hate speech have received increasing attention. A recurring question is whether the occurrence of extreme events offline systematically triggers bursts of hate speech online, indicated by peaks in the volume of hateful social media posts. Formally, this question translates into measuring the association between a sparse event series and a time series. We propose a novel statistical methodology to measure, test and visualize the systematic association between rare events and peaks in a time series. In contrast to previous methods for causal inference or independence tests on time series, our approach focuses only on the timing of events and peaks and no other distributional characteristics. We follow the framework of event coincidence analysis (ECA) that was originally developed to correlate point processes. We formulate a discrete-time variant of ECA and derive all required distributions to enable analyses of peaks in time series with a special focus on serial dependencies and peaks over multiple thresholds. The analysis gives rise to a novel visualization of the association via quantile-trigger rate plots. We demonstrate the utility of our approach by analyzing whether Islamist terrorist attacks in Western Europe and North America systematically trigger bursts of hate speech and counter-hate speech on Twitter.
References
Alvi, H. (2014). The diffusion of intra-Islamic violence and terrorism: The impact of the proliferation of Salafi/Wahhabi ideologies. Middle East Rev. Int. Aff. 18 38–50.Alvi, H. (2014). The diffusion of intra-Islamic violence and terrorism: The impact of the proliferation of Salafi/Wahhabi ideologies. Middle East Rev. Int. Aff. 18 38–50.
Bartlett, J. and Miller, C. (2012). The edge of violence: Towards telling the difference between violent and non-violent radicalization. Terrorism Polit. Violence 24 1–21.Bartlett, J. and Miller, C. (2012). The edge of violence: Towards telling the difference between violent and non-violent radicalization. Terrorism Polit. Violence 24 1–21.
Bennett, W. L. (2005). Social movements beyond borders: Organization, communication, and political capacity in two eras of transnational activism. In Transnational Protest and Global Activism (D. Della Porta and S. Tarrow, eds.) 203–226. Rowman & Littlefield Publishers, Inc., Lanham, MD, USA.Bennett, W. L. (2005). Social movements beyond borders: Organization, communication, and political capacity in two eras of transnational activism. In Transnational Protest and Global Activism (D. Della Porta and S. Tarrow, eds.) 203–226. Rowman & Littlefield Publishers, Inc., Lanham, MD, USA.
Besserve, M., Logothetis, N. K. and Schölkopf, B. (2013). Statistical analysis of coupled time series with kernel cross-spectral density operators. In Advances in Neural Information Processing Systems (NIPS).Besserve, M., Logothetis, N. K. and Schölkopf, B. (2013). Statistical analysis of coupled time series with kernel cross-spectral density operators. In Advances in Neural Information Processing Systems (NIPS).
Box, G. E. P. and Tiao, G. C. (1975). Intervention analysis with applications to economic and environmental problems. J. Amer. Statist. Assoc. 70 70–79. 0316.62045 10.1080/01621459.1975.10480264Box, G. E. P. and Tiao, G. C. (1975). Intervention analysis with applications to economic and environmental problems. J. Amer. Statist. Assoc. 70 70–79. 0316.62045 10.1080/01621459.1975.10480264
Brodersen, K. H., Gallusser, F., Koehler, J., Remy, N. and Scott, S. L. (2015). Inferring causal impact using Bayesian structural time-series models. Ann. Appl. Stat. 9 247–274. 06446568 10.1214/14-AOAS788 euclid.aoas/1430226092Brodersen, K. H., Gallusser, F., Koehler, J., Remy, N. and Scott, S. L. (2015). Inferring causal impact using Bayesian structural time-series models. Ann. Appl. Stat. 9 247–274. 06446568 10.1214/14-AOAS788 euclid.aoas/1430226092
Burnap, P. and Williams, M. L. (2014). Hate speech, machine classification and statistical modelling of information flows on Twitter: Interpretation and communication for policy decision making. In Proceedings of the Internet, Policy and Politics Conference (IPP).Burnap, P. and Williams, M. L. (2014). Hate speech, machine classification and statistical modelling of information flows on Twitter: Interpretation and communication for policy decision making. In Proceedings of the Internet, Policy and Politics Conference (IPP).
Burnap, P. and Williams, M. L. (2016). Us and them: Identifying cyber hate on Twitter across multiple protected characteristics. EPJ Data Sci. 5 1–15.Burnap, P. and Williams, M. L. (2016). Us and them: Identifying cyber hate on Twitter across multiple protected characteristics. EPJ Data Sci. 5 1–15.
Burnap, P., Williams, M. L., Sloan, L., Rana, O., Housley, W., Edwards, A., Knight, V., Procter, R. and Voss, A. (2014). Tweeting the terror: Modelling the social media reaction to the Woolwich terrorist attack. Soc. Netw. Anal. Min. 4 1–14.Burnap, P., Williams, M. L., Sloan, L., Rana, O., Housley, W., Edwards, A., Knight, V., Procter, R. and Voss, A. (2014). Tweeting the terror: Modelling the social media reaction to the Woolwich terrorist attack. Soc. Netw. Anal. Min. 4 1–14.
Cehajic, S. and Brown, R. (2008). Not in my name: A social psychological study of antecedents and consequences of acknowledgment of in-group atrocities. Genocide Stud. Prev. 3 195–211.Cehajic, S. and Brown, R. (2008). Not in my name: A social psychological study of antecedents and consequences of acknowledgment of in-group atrocities. Genocide Stud. Prev. 3 195–211.
Chandrasekharan, E., Pavalanathan, U., Srinivasan, A., Glynn, A., Eistenstein, J. and Gilbert, E. (2017). You can’t stay here: The efficacy of reddit’s 2015 ban examined through hate speech. Proc. ACM Human-Comput. Interact. 1 31:1–31:22.Chandrasekharan, E., Pavalanathan, U., Srinivasan, A., Glynn, A., Eistenstein, J. and Gilbert, E. (2017). You can’t stay here: The efficacy of reddit’s 2015 ban examined through hate speech. Proc. ACM Human-Comput. Interact. 1 31:1–31:22.
Chwialkowski, K. and Gretton, A. (2014). A kernel independence test for random processes. In Proceedings of the 31st International Conference on Machine Learning (ICML).Chwialkowski, K. and Gretton, A. (2014). A kernel independence test for random processes. In Proceedings of the 31st International Conference on Machine Learning (ICML).
Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer Series in Statistics. Springer London, Ltd., London. 0980.62043Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer Series in Statistics. Springer London, Ltd., London. 0980.62043
Cunha, T. O., Weber, I. and Pappa, G. L. (2017). A warm welcome matters! The link between social feedback and weight loss in /r/loseit. In Proceedings of the 26th International Conference on World Wide Web (WWW).Cunha, T. O., Weber, I. and Pappa, G. L. (2017). A warm welcome matters! The link between social feedback and weight loss in /r/loseit. In Proceedings of the 26th International Conference on World Wide Web (WWW).
Davidson, H. (2014). ‘Not in my name’ campaign organiser warns of danger of political rhetoric. The Guardian. Available at https://www.theguardian.com/australia-news/2014/oct/03/not-in-my-name-campaign-organiser-warns-of-danger-of-political-rhetoric, 2014-10-03.Davidson, H. (2014). ‘Not in my name’ campaign organiser warns of danger of political rhetoric. The Guardian. Available at https://www.theguardian.com/australia-news/2014/oct/03/not-in-my-name-campaign-organiser-warns-of-danger-of-political-rhetoric, 2014-10-03.
Davidson, T., Warmsley, D., Macy, M. and Weber, I. (2017). Automated hate speech detection and the problem of offensive language. In Proceedings of the 11th International Conference on Web and Social Media (ICWSM).Davidson, T., Warmsley, D., Macy, M. and Weber, I. (2017). Automated hate speech detection and the problem of offensive language. In Proceedings of the 11th International Conference on Web and Social Media (ICWSM).
Davison, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and Their Application. Cambridge Series in Statistical and Probabilistic Mathematics 1. Cambridge Univ. Press, Cambridge.Davison, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and Their Application. Cambridge Series in Statistical and Probabilistic Mathematics 1. Cambridge Univ. Press, Cambridge.
De Koster, W. and Houtman, D. (2008). ‘Stormfront is like a second home to me.’ On virtual community formation by right-wing extremists. Inf. Commun. Soc. 11 1155–1176.De Koster, W. and Houtman, D. (2008). ‘Stormfront is like a second home to me.’ On virtual community formation by right-wing extremists. Inf. Commun. Soc. 11 1155–1176.
De Smedt, T., De Pauw, G. and Van Ostaeyen, P. (2018). Automatic detection of online jihadist hate speech. Technical report, CLiPS Research Center, Univ. Antwerp.De Smedt, T., De Pauw, G. and Van Ostaeyen, P. (2018). Automatic detection of online jihadist hate speech. Technical report, CLiPS Research Center, Univ. Antwerp.
Dewey, C. (2016). #StopIslam Twitter-trended for all the right reasons. Washington Post. Available at https://www.washingtonpost.com/news/the-intersect/wp/2016/03/22/stopislam-twitter-trended-for-all-the-right-reasons/, 2016-03-22.Dewey, C. (2016). #StopIslam Twitter-trended for all the right reasons. Washington Post. Available at https://www.washingtonpost.com/news/the-intersect/wp/2016/03/22/stopislam-twitter-trended-for-all-the-right-reasons/, 2016-03-22.
Djuric, N., Zhou, J., Morris, R., Grbovic, M., Radosavljevic, V. and Bhamidipati, N. (2015). Hate speech detection with comment embeddings. In Proceedings of Th 24th International Conference on World Wide Web (WWW).Djuric, N., Zhou, J., Morris, R., Grbovic, M., Radosavljevic, V. and Bhamidipati, N. (2015). Hate speech detection with comment embeddings. In Proceedings of Th 24th International Conference on World Wide Web (WWW).
Donges, J. F., Schleusner, C. F., Siegmund, J. F. and Donner, R. V. (2016). Event coincidence analysis for quantifying statistical interrelationships between event time series: On the role of flood events as triggers of epidemic outbreaks. Eur. Phys. J. Spec. Top. 487 471–487.Donges, J. F., Schleusner, C. F., Siegmund, J. F. and Donner, R. V. (2016). Event coincidence analysis for quantifying statistical interrelationships between event time series: On the role of flood events as triggers of epidemic outbreaks. Eur. Phys. J. Spec. Top. 487 471–487.
Dudoit, S. and van der Laan, M. J. (2008). Multiple Testing Procedures with Applications to Genomics. Springer Series in Statistics. Springer, New York. 1261.62014Dudoit, S. and van der Laan, M. J. (2008). Multiple Testing Procedures with Applications to Genomics. Springer Series in Statistics. Springer, New York. 1261.62014
ElSherief, M., Nilizadeh, S., Nguyen, D., Vigna, G. and Belding, E. (2018a). Peer to peer hate: Hate speech instigators and their targets. In Proceedings of the 12th International AAAI Conference on Web and Social Media (ICWSM).ElSherief, M., Nilizadeh, S., Nguyen, D., Vigna, G. and Belding, E. (2018a). Peer to peer hate: Hate speech instigators and their targets. In Proceedings of the 12th International AAAI Conference on Web and Social Media (ICWSM).
ElSherief, M., Kulkarni, V., Nguyen, D., Wang, W. Y. and Belding, E. (2018b). Hate lingo: A target-based linguistic analysis of hate speech in social media. In Proceedings of the 12th International AAAI Conference on Web and Social Media (ICWSM).ElSherief, M., Kulkarni, V., Nguyen, D., Wang, W. Y. and Belding, E. (2018b). Hate lingo: A target-based linguistic analysis of hate speech in social media. In Proceedings of the 12th International AAAI Conference on Web and Social Media (ICWSM).
National Consortium for the Study of Terrorism (2018). Global terrorism database [2014–2017]. Available at https://www.start.umd.edu/gtd.National Consortium for the Study of Terrorism (2018). Global terrorism database [2014–2017]. Available at https://www.start.umd.edu/gtd.
Frahm, G., Junker, M. and Schmidt, R. (2005). Estimating the tail-dependence coefficient: Properties and pitfalls. Insurance Math. Econom. 37 80–100. 1101.62012 10.1016/j.insmatheco.2005.05.008Frahm, G., Junker, M. and Schmidt, R. (2005). Estimating the tail-dependence coefficient: Properties and pitfalls. Insurance Math. Econom. 37 80–100. 1101.62012 10.1016/j.insmatheco.2005.05.008
Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37 424–438. 1366.91115 10.2307/1912791Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37 424–438. 1366.91115 10.2307/1912791
Hemmings, C. (2016). From #StopIslam to Allison Pearson and Katie Hopkins, the social media response to Brussels has been shocking. The Independent. Available at https://www.independent.co.uk/voices/from-stopislam-to-allison-pearson-and-katie-hopkins-the-social-media-response-to-brussels-has-been-a6946116.html, 2016-03-22.Hemmings, C. (2016). From #StopIslam to Allison Pearson and Katie Hopkins, the social media response to Brussels has been shocking. The Independent. Available at https://www.independent.co.uk/voices/from-stopislam-to-allison-pearson-and-katie-hopkins-the-social-media-response-to-brussels-has-been-a6946116.html, 2016-03-22.
Krishnan, M. (2017). ‘Not in my name’—Indians protest vigilante attacks on Muslims. Deutsche Welle. Available at https://p.dw.com/p/2fYJP, 2017-06-29.Krishnan, M. (2017). ‘Not in my name’—Indians protest vigilante attacks on Muslims. Deutsche Welle. Available at https://p.dw.com/p/2fYJP, 2017-06-29.
Kwok, I. and Wang, Y. (2013). Locate the hate: Detecting tweets against blacks. In Proceedings of the 27th AAAI Conference on Artificial Intelligence (AAAI).Kwok, I. and Wang, Y. (2013). Locate the hate: Detecting tweets against blacks. In Proceedings of the 27th AAAI Conference on Artificial Intelligence (AAAI).
Magdy, W., Darwish, K. and Abokhodair, N. (2015). Quantifying public response towards Islam on Twitter after Paris attacks. Preprint. Available at arXiv:1512.04570. 1512.04570Magdy, W., Darwish, K. and Abokhodair, N. (2015). Quantifying public response towards Islam on Twitter after Paris attacks. Preprint. Available at arXiv:1512.04570. 1512.04570
Matias, J. N., Johnson, A., Boesel, W. E., Keegan, B., Friedman, J. and DeTar, C. (2015). Reporting, Reviewing, and Responding to Harassment on Twitter. Women, Action, and the Media.Matias, J. N., Johnson, A., Boesel, W. E., Keegan, B., Friedman, J. and DeTar, C. (2015). Reporting, Reviewing, and Responding to Harassment on Twitter. Women, Action, and the Media.
Mondal, M., Silva, L. A. and Benevenuto, F. (2017). A measurement study of hate speech in social media. In Proceedings of the 28th ACM Conference on Hypertext and Social Media (HT).Mondal, M., Silva, L. A. and Benevenuto, F. (2017). A measurement study of hate speech in social media. In Proceedings of the 28th ACM Conference on Hypertext and Social Media (HT).
Olteanu, A., Castillo, C., Boy, J. and Varshney, K. R. (2018). The effect of extremist violence on hateful speech online. In Proceedings of the 12th International AAAI Conference on Web and Social Media (ICWSM).Olteanu, A., Castillo, C., Boy, J. and Varshney, K. R. (2018). The effect of extremist violence on hateful speech online. In Proceedings of the 12th International AAAI Conference on Web and Social Media (ICWSM).
Quiroga, R. Q., Kreuz, T. and Grassberger, P. (2002). Event synchronization: A simple and fast method to measure synchronicity and time delay patterns. Phys. Rev. E (3) 66 041904, 9.Quiroga, R. Q., Kreuz, T. and Grassberger, P. (2002). Event synchronization: A simple and fast method to measure synchronicity and time delay patterns. Phys. Rev. E (3) 66 041904, 9.
Ribeiro, M. H., Calais, P. H., Santos, Y. A., Almeida, V. A. F. and Meira, W. (2018). Characterizing and detecting hateful users on Twitter. In Proceedings of the 12th International AAAI Conference on Web and Social Media (ICWSM).Ribeiro, M. H., Calais, P. H., Santos, Y. A., Almeida, V. A. F. and Meira, W. (2018). Characterizing and detecting hateful users on Twitter. In Proceedings of the 12th International AAAI Conference on Web and Social Media (ICWSM).
Saha, K., Chandrasekharan, E. and De Choudhury, M. (2019). Prevalence and psychological effects of hateful speech in online college communities. In Proceedings of the 11th ACM Conference on Web Science (WebSci).Saha, K., Chandrasekharan, E. and De Choudhury, M. (2019). Prevalence and psychological effects of hateful speech in online college communities. In Proceedings of the 11th ACM Conference on Web Science (WebSci).
Scharwächter, E. and Müller, E. (2020). Two-sample testing for event impacts in time series. In Proceedings of the SIAM International Conference on Data Mining (SIAM SDM).Scharwächter, E. and Müller, E. (2020). Two-sample testing for event impacts in time series. In Proceedings of the SIAM International Conference on Data Mining (SIAM SDM).
Scharwächter, E. and Müller, E. (2020). Supplement to “Does terrorism trigger online hate speech? On the association of events and time series.” https://doi.org/10.1214/20-AOAS1338SUPPScharwächter, E. and Müller, E. (2020). Supplement to “Does terrorism trigger online hate speech? On the association of events and time series.” https://doi.org/10.1214/20-AOAS1338SUPP
Schleussner, C.-F., Donges, J. F., Donner, R. V. and Schellnhuber, H. J. (2016). Armed-conflict risks enhanced by climate-related disasters in ethnically fractionalized countries. Proc. Natl. Acad. Sci. USA 113 9216–9221.Schleussner, C.-F., Donges, J. F., Donner, R. V. and Schellnhuber, H. J. (2016). Armed-conflict risks enhanced by climate-related disasters in ethnically fractionalized countries. Proc. Natl. Acad. Sci. USA 113 9216–9221.
Schmidt, A. and Wiegand, M. (2017). A survey on hate speech detection using natural language processing. In Proceedings of the 5th International Workshop on Natural Language Processing for Social Media (SocialNLP).Schmidt, A. and Wiegand, M. (2017). A survey on hate speech detection using natural language processing. In Proceedings of the 5th International Workshop on Natural Language Processing for Social Media (SocialNLP).
Siegmund, J. F., Sanders, T. G. M., Heinrich, I., van der Maaten, E., Simard, S., Helle, G. and Donner, R. V. (2016). Meteorological drivers of extremes in daily stem radius variations of beech, oak, and pine in northeastern Germany: An event coincidence analysis. Front. Plant Sci. 7 733.Siegmund, J. F., Sanders, T. G. M., Heinrich, I., van der Maaten, E., Simard, S., Helle, G. and Donner, R. V. (2016). Meteorological drivers of extremes in daily stem radius variations of beech, oak, and pine in northeastern Germany: An event coincidence analysis. Front. Plant Sci. 7 733.
Silva, L., Mondal, M., Correa, D., Benevenuto, F. and Weber, I. (2016). Analyzing the targets of hate in online social media. In Proceedings of the 10th International Conference on Web and Social Media (ICWSM).Silva, L., Mondal, M., Correa, D., Benevenuto, F. and Weber, I. (2016). Analyzing the targets of hate in online social media. In Proceedings of the 10th International Conference on Web and Social Media (ICWSM).
Warner, W. and Hirschberg, J. (2012). Detecting hate speech on the World Wide Web. In Proceedings of the 2nd Workshop on Language in Social Media (LSM).Warner, W. and Hirschberg, J. (2012). Detecting hate speech on the World Wide Web. In Proceedings of the 2nd Workshop on Language in Social Media (LSM).
Williams, M. L. and Burnap, P. (2016). Cyberhate on social media in the aftermath of Woolwich: A case study in computational criminology and big data. Br. J. Criminol. 56 211–238.Williams, M. L. and Burnap, P. (2016). Cyberhate on social media in the aftermath of Woolwich: A case study in computational criminology and big data. Br. J. Criminol. 56 211–238.
Yan, X., Wu, Q. and Zhang, W. (2019). Cross-sectional learning of extremal dependence among financial assets. In Neural Information Processing Systems.Yan, X., Wu, Q. and Zhang, W. (2019). Cross-sectional learning of extremal dependence among financial assets. In Neural Information Processing Systems.
