Extended Laplace approximation for self-exciting spatio-temporal models of count data

Anderson, 1987, Temperature and aggression: effects on quarterly, yearly, and city rates of violent and nonviolent crime, J. Personal. Soc. Psychol., 52, 1161, 10.1037/0022-3514.52.6.1161 Betancourt, 2016 Bivand, 2018, Comparing implementations of global and local indicators of spatial association, TEST, 27, 716, 10.1007/s11749-018-0599-x Brillinger, 1983, Maximum likelihood estimation in a latent variable problem, 31 Carroll, 2015, Comparing inla and openbugs for hierarchical poisson modeling in disease mapping, Spat. Spatio Temporal Epidemiol., 14, 45, 10.1016/j.sste.2015.08.001 Clark, 2018 Clark, 2018, Modeling and estimation for self-exciting spatio-temporal models of terrorist activity, Ann. Appl. Stat., 12, 633, 10.1214/17-AOAS1112 Clark, 2021, A class of spatially correlated self-exciting statistical models, Spat. Stat., 43, 10.1016/j.spasta.2021.100493 Cressie, 2015 Cressie, 2015 D’Angelo, 2022, Self-exciting point process modelling of crimes on linear networks, Stat. Model., 10.1177/1471082X221094146 Davis, 2016 Embrechts, 2011, Multivariate hawkes processes: an application to financial data, J. Appl. Probab., 48, 367, 10.1239/jap/1318940477 Escudero, 2022, A spatially correlated model with generalized autoregressive conditionally heteroskedastic structure for counts of crimes, Entropy, 24, 892, 10.3390/e24070892 Evangelou, 2011, Estimation and prediction for spatial generalized linear mixed models using high order laplace approximation, J. Statist. Plann. Inference, 141, 3564, 10.1016/j.jspi.2011.05.008 Ferkingstad, 2015, Improving the inla approach for approximate bayesian inference for latent gaussian models, Electron. J. Stat., 9, 2706, 10.1214/15-EJS1092 Fokianos, 2009, Poisson autoregression, J. Amer. Statist. Assoc., 104, 1430, 10.1198/jasa.2009.tm08270 Fox, 2016 Gabriel, 2022, stpp: Space-time point pattern simulation, Vis. Anal. Gelman, 2015, Stan: A probabilistic programming language for bayesian inference and optimization, J. Educ. Behav. Stat., 40, 530, 10.3102/1076998615606113 Jin, 2005, Generalized hierarchical multivariate car models for areal data, Biometrics, 61, 950, 10.1111/j.1541-0420.2005.00359.x Joe, 2008, Accuracy of laplace approximation for discrete response mixed models, Comput. Statist. Data Anal., 52, 5066, 10.1016/j.csda.2008.05.002 Joseph, 2016, Exact sparse car models in stan, Stan Case Stud., 3 Martins, 2013, Bayesian computing with inla: new features, Comput. Statist. Data Anal., 67, 68, 10.1016/j.csda.2013.04.014 Mohler, 2013, Modeling and estimation of multi-source clustering in crime and security data, Ann. Appl. Stat., 152, 5 Mohler, 2014, Marked point process hotspot maps for homicide and gun crime prediction in Chicago, Int. J. Forecast., 30, 491, 10.1016/j.ijforecast.2014.01.004 Park, 2021, Investigating clustering and violence interruption in gang-related violent crime data using spatial–temporal point processes with covariates, J. Amer. Statist. Assoc., 116, 1674, 10.1080/01621459.2021.1898408 R Core Team, 2023 Raudenbush, 2000, Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate laplace approximation, J. Comput. Graph. Statist., 9, 141 Reinhart, 2018, A review of self-exciting spatio-temporal point processes and their applications, Statist. Sci., 33, 299 Reinhart, 2018, Self-exciting point processes with spatial covariates, J. R. Stat. Soc. Ser. C, 67, 1305, 10.1111/rssc.12277 Rue, 2009, Approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations, J. R. Stat. Soc. Ser. B Stat. Methodol., 71, 319, 10.1111/j.1467-9868.2008.00700.x Rue, 2017, Bayesian computing with inla: a review, Annu. Rev. Stat. Appl., 4, 395, 10.1146/annurev-statistics-060116-054045 Shun, 1995, Laplace approximation of high dimensional integrals, J. R. Stat. Soc. Ser. B Stat. Methodol., 57, 749 Spiegelhalter, 1998 Tierney, 1986, Accurate approximations for posterior moments and marginal densities, J. Amer. Statist. Assoc., 81, 82, 10.1080/01621459.1986.10478240 Wall, 2004, A close look at the spatial structure implied by the car and sar models, J. Statist. Plann. Inference, 121, 311, 10.1016/S0378-3758(03)00111-3 Wikle, 2019 Zhuang, 2018, A Semiparametric Spatiotemporal Hawkes-Type Point Process Model with Periodic Background for Crime Data, J. R. Stat. Soc. Ser. A, 182, 919, 10.1111/rssa.12429