Spatio-temporal point process statistics: A review

Jonatan A. González*, Francisco J. Rodríguez-Cortés, Ottmar Cronie, Jorge Mateu

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

65 Scopus citations


Spatio-temporal point process data have been analysed quite a bit in specialised fields, with the aim of better understanding the inherent mechanisms that govern the temporal evolution of events placed in a planar region. In particular, in the last decade there has been an acceleration of methodological developments, accompanied by a broad collection of applications as spatio-temporally indexed data have become more widely available in many scientific fields. We present a self-contained review describing statistical models and methods that can be used to analyse patterns of points in space and time when the questions of scientific interest concern both their spatial and their temporal behaviour. We revisit moment characteristics that define summary statistics, as well as conditional intensities which uniquely characterise certain spatio-temporal point processes. We make use of these concepts to describe models and associated methods of inference for spatio-temporal point process data. Three new motivating real-data examples are described and analysed throughout the paper to illustrate the most relevant techniques, discussing the pros and cons of the different considered approaches.

Original languageEnglish (US)
Pages (from-to)505-544
Number of pages40
JournalSpatial Statistics
StatePublished - Nov 1 2016

Bibliographical note

Funding Information:
Work partially funded by Grant MTM2013-43917-P from the Spanish Ministry of Science and Education , and Grant P1-1B2015-40 from University Jaume I .

Publisher Copyright:
© 2016 Elsevier B.V.


  • Edge-correction
  • Empirical models
  • Intensity function
  • Mechanistic models
  • Second-order properties
  • Separability

ASJC Scopus subject areas

  • Statistics and Probability
  • Computers in Earth Sciences
  • Management, Monitoring, Policy and Law


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