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Modeling Conflict Dynamics with Spatio-temporal Data

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSMATHMETH))

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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.

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Notes

  1. 1.

    We only consider the slightly restrictive assumption that the measure admits a density.

  2. 2.

    The logarithm is used to ensure positivity of the resulting intensity function.

  3. 3.

    This is not to be confused with the method of moments associated with parameter estimation.

  4. 4.

    The whole field of graphical models and graphical statistics is concerned with inference algorithms for probability distributions exhibiting specific conditional independence relationships, cf. Bishop (2006).

  5. 5.

    For point processes we define \({{\varvec{y}}}_k\) as the spatial coordinates of points in \(\fancyscript{Y}_k\).

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Author information

Authors and Affiliations

  1. School of Geographical Sciences/Department of Mathematics, The University of Bristol, University Road, Bristol, UK

    Andrew Zammit-Mangion

  2. R & D Lab, New York Times, New York, NY, 10036, USA

    Michael Dewar

  3. Automatic Control an Systems Engineering, The University of Sheffield, Mappin Street, Sheffield, UK

    Visakan Kadirkamanathan

  4. German Institute of Global and Area Studies, Hamburg, Germany

    Anaïd Flesken

  5. School of Informatics, University of Edinburgh, Edinburgh, UK

    Guido Sanguinetti

Authors
  1. Andrew Zammit-Mangion
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  2. Michael Dewar
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  3. Visakan Kadirkamanathan
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  4. Anaïd Flesken
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  5. Guido Sanguinetti
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Correspondence to Andrew Zammit-Mangion .

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Zammit-Mangion, A., Dewar, M., Kadirkamanathan, V., Flesken, A., Sanguinetti, G. (2013). Theory. In: Modeling Conflict Dynamics with Spatio-temporal Data. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-319-01038-0_2

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