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State estimation for aoristic models

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  • Maria N. M. van Lieshout
  • Robin L. Markwitz

Abstract

Aoristic data can be described by a marked point process in time in which the points cannot be observed directly but are known to lie in observable intervals, the marks. We consider Bayesian state estimation for the latent points when the marks are modeled in terms of an alternating renewal process in equilibrium and the prior is a Markov point process. We derive the posterior distribution, estimate its parameters and present some examples that illustrate the influence of the prior distribution. The model is then used to estimate times of occurrence of interval censored crimes.

Suggested Citation

  • Maria N. M. van Lieshout & Robin L. Markwitz, 2023. "State estimation for aoristic models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1068-1089, September.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:1068-1089
    DOI: 10.1111/sjos.12619
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    References listed on IDEAS

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    1. Roberts, G. O. & Smith, A. F. M., 1994. "Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms," Stochastic Processes and their Applications, Elsevier, vol. 49(2), pages 207-216, February.
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