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Estimation of space-time self-exciting point process models using multi-dimensional Gaussian-type exponent

Edward Appau Nketiah1, Chenlong Li1, Weihua Yang1

  • 1College of Mathematics, Taiyuan University of Technology, Jinzhong, Shanxi, China.

Plos One
|April 2, 2026
PubMed
Summary
This summary is machine-generated.

Space-time self-exciting point process models effectively analyze crime data clustering. A new Gaussian-type exponent approximation method overcomes computational challenges for large datasets, revealing burglary patterns.

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Area of Science:

  • Statistics
  • Criminology
  • Data Science

Background:

  • Space-time self-exciting point process models are effective for analyzing clustered data, including crime, financial, and seismic datasets.
  • Previous applications to large crime datasets were limited by inflexible conditional intensity function estimation and computational challenges.

Purpose of the Study:

  • To adapt space-time self-exciting point process models for large-scale crime data analysis.
  • To introduce a flexible and computationally efficient estimation method for these models.

Main Methods:

  • Proposed a multi-dimensional Gaussian-type exponent approximation method.
  • Evaluated the method through simulations.
  • Applied the method to analyze space-time burglary patterns in Chicago, Illinois.

Main Results:

  • The proposed method demonstrated flexibility in estimating the conditional intensity function.
  • Computational difficulties associated with large datasets were overcome.
  • A significant space-time clustering phenomenon was identified in Chicago burglary data.

Conclusions:

  • The novel approximation method enhances the applicability of space-time self-exciting point process models for large crime datasets.
  • The study confirms the utility of these models for uncovering spatial and temporal crime patterns.