Extended Laplace approximation for self-exciting spatio-temporal models of count data
dc.contributor.author | Clark, Nicholas | |
dc.contributor.author | Dixon, Philip | |
dc.contributor.author | Dixon, Philip | |
dc.contributor.department | Statistics | |
dc.date | 2019-06-26T00:59:43.000 | |
dc.date.accessioned | 2020-07-02T06:56:02Z | |
dc.date.available | 2020-07-02T06:56:02Z | |
dc.date.issued | 2017-09-28 | |
dc.description.abstract | <p>Self-Exciting models are statistical models of count data where the probability of an event occurring is infl d by the history of the process. In particular, self-exciting spatio-temporal models allow for spatial dependence as well as temporal self-excitation. For large spatial or temporal regions, however, the model leads to an intractable likeli- hood. An increasingly common method for dealing with large spatio-temporal models is by using Laplace approximations (LA). This method is convenient as it can easily be applied and is quickly implemented. However, as we will demonstrate in this manuscript, when applied to self-exciting Poisson spatial-temporal models, Laplace Approximations result in a significant bias in estimating some parameters. Due to this bias, we propose using up to sixth-order corrections to the LA for fi these models. We will demonstrate how to do this in a Bayesian setting for Self-Exciting Spatio-Temporal models. We will further show there is a limited parameter space where the extended LA method still has bias. In these uncommon instances we will demonstrate how amore computationally intensive fully Bayesian approach using the Stan software program is possible in those rare instances. The performance of the extended LA method is illustrated with both simulation and real-world data.</p> | |
dc.description.comments | This is the preprint of an article published as Clark, Nicholas J., and Philip M. Dixon. "Extended Laplace approximation for self-exciting spatio-temporal models of count data." Spatial Statistics 56 (2023): 100762. doi:10.1016/j.spasta.2023.100762. © 2023 Elsevier B.V. Posted with permission. | |
dc.identifier | archive/lib.dr.iastate.edu/stat_las_preprints/143/ | |
dc.identifier.articleid | 1142 | |
dc.identifier.contextkey | 14405299 | |
dc.identifier.s3bucket | isulib-bepress-aws-west | |
dc.identifier.submissionpath | stat_las_preprints/143 | |
dc.identifier.uri | https://dr.lib.iastate.edu/handle/20.500.12876/90304 | |
dc.language.iso | en | |
dc.source.bitstream | archive/lib.dr.iastate.edu/stat_las_preprints/143/2017_Dixon_ExtendedLaplacePreprint.pdf|||Fri Jan 14 20:18:08 UTC 2022 | |
dc.source.uri | https://doi.org/10.1016/j.spasta.2023.100762 | |
dc.subject.disciplines | Criminology and Criminal Justice | |
dc.subject.disciplines | Numerical Analysis and Computation | |
dc.subject.disciplines | Statistical Models | |
dc.subject.disciplines | Statistics and Probability | |
dc.subject.keywords | Asymptotic Bias | |
dc.subject.keywords | Intractable Likelihoods | |
dc.subject.keywords | Terrorism and Crime | |
dc.title | Extended Laplace approximation for self-exciting spatio-temporal models of count data | |
dc.title.alternative | An Extended Laplace Approximation Method for Bayesian Inference of Self-Exciting Spatial-Temporal Models of Count Data | |
dc.type | article | |
dc.type.genre | article | |
dspace.entity.type | Publication | |
relation.isAuthorOfPublication | 7b3eb8d2-a569-4aba-87a1-5d9c2d99fade | |
relation.isOrgUnitOfPublication | 264904d9-9e66-4169-8e11-034e537ddbca |
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