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Estimation of spatiotemporal poisson processes with missing data.

Vincent Guigues1, Anton Kleywegt2, Victor Hugo Nascimento3

  • 1School of Applied Mathematics, FGV, Rio de Janeiro, Brazil. vincent.guigues@fgv.br.

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|April 25, 2026
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This study introduces four models for spatiotemporal Poisson processes with missing location data, demonstrating their effectiveness in analyzing emergency calls and improving data accuracy.

Keywords:
Missing dataRegressionRegularized likelihood estimatorSpatiotemporal data

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Area of Science:

  • Statistics
  • Data Science
  • Epidemiology

Background:

  • Spatiotemporal Poisson processes are crucial for analyzing event data over space and time.
  • Missing location data in event reporting, such as emergency calls, poses significant analytical challenges.
  • Existing models may not adequately address the complexities introduced by incomplete spatial information.

Purpose of the Study:

  • To develop and evaluate statistical models for spatiotemporal Poisson processes that can handle missing location data.
  • To assess the impact of accounting for missing location data on the analysis of real-world event data.
  • To provide a framework for handling both missing location and timestamp data in spatiotemporal analyses.

Main Methods:

  • Four distinct statistical models were developed to accommodate missing location data within spatiotemporal Poisson process frameworks.
  • Model estimation techniques were applied to these proposed models.
  • The models were validated using a dataset of emergency medical service call arrivals, a scenario characterized by frequent omissions of emergency locations.
  • Methods for developing models to address missing timestamp data were also explored.

Main Results:

  • The study demonstrates that models incorporating provisions for missing location data yield different and more accurate results compared to analyses that ignore this missingness.
  • The application to emergency call data highlights the practical significance of these models in real-world scenarios.
  • The developed models provide a robust approach to analyzing spatiotemporal data with incomplete location information.

Conclusions:

  • Accounting for missing location data in spatiotemporal Poisson process models is essential for accurate event analysis.
  • The proposed models offer a valuable tool for researchers and practitioners dealing with incomplete spatiotemporal datasets.
  • The findings underscore the importance of developing sophisticated statistical methods to handle data imperfections in fields like emergency response and public health.