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Theory

Journal Article


Abstract


  • This chapter lays the theoretical foundations for the approach to spatio-temporal modeling from data typically found in conflict data sets. The chapter begins by outlining the basic principles of point-process theory, starting from the definition of the Poisson distribution and ending with a description of the log-Gaussian Cox process and the point-process likelihood function. The chapter proceeds to discuss two important classes of spatio-temporal models, the stochastic partial differential equation (SPDE) and the stochastic integro-difference equation (SIDE). Dimensionality reduction techniques to reduce these models into state-space form are then given. Recrusive estimation algorithms for estimation with a state-space model are then derived and are followed by a strategy to include unknown parameters within the estimation framework through variational Bayes. The chapter concludes with a section on implementation tools. This includes details on non-parametric methods for obtaining descriptive statistics from events, a basis function placement method and a variational-Laplace algorithm for inference under the point-process likelihood.

Publication Date


  • 2013

Citation


  • Zammit-Mangion, A., Dewar, M., Kadirkamanathan, V., Flesken, A., & Sanguinetti, G. (2013). Theory. SpringerBriefs in Applied Sciences and Technology, (9783319010373), 15-46. doi:10.1007/978-3-319-01038-0_2

Scopus Eid


  • 2-s2.0-85028854129

Web Of Science Accession Number


Start Page


  • 15

End Page


  • 46

Issue


  • 9783319010373

Abstract


  • This chapter lays the theoretical foundations for the approach to spatio-temporal modeling from data typically found in conflict data sets. The chapter begins by outlining the basic principles of point-process theory, starting from the definition of the Poisson distribution and ending with a description of the log-Gaussian Cox process and the point-process likelihood function. The chapter proceeds to discuss two important classes of spatio-temporal models, the stochastic partial differential equation (SPDE) and the stochastic integro-difference equation (SIDE). Dimensionality reduction techniques to reduce these models into state-space form are then given. Recrusive estimation algorithms for estimation with a state-space model are then derived and are followed by a strategy to include unknown parameters within the estimation framework through variational Bayes. The chapter concludes with a section on implementation tools. This includes details on non-parametric methods for obtaining descriptive statistics from events, a basis function placement method and a variational-Laplace algorithm for inference under the point-process likelihood.

Publication Date


  • 2013

Citation


  • Zammit-Mangion, A., Dewar, M., Kadirkamanathan, V., Flesken, A., & Sanguinetti, G. (2013). Theory. SpringerBriefs in Applied Sciences and Technology, (9783319010373), 15-46. doi:10.1007/978-3-319-01038-0_2

Scopus Eid


  • 2-s2.0-85028854129

Web Of Science Accession Number


Start Page


  • 15

End Page


  • 46

Issue


  • 9783319010373