State estimation for aoristic models

Marie-Colette van Lieshout; Robin Luca Markwitz

doi:10.1111/sjos.12619

State estimation for aoristic models

Marie-Colette van Lieshout, Robin Luca Markwitz^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

2 Citations (Scopus)

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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.

Original language	English
Pages (from-to)	1068-1089
Number of pages	22
Journal	Scandinavian journal of statistics
Volume	50
Issue number	3
Early online date	4 Oct 2022
DOIs	https://doi.org/10.1111/sjos.12619
Publication status	Published - 1 Sept 2023

Keywords

UT-Hybrid-D
Aoristic data
Criminological data
Marked temporal point process
Markov chain Monte Carlo methods
Markov point process state estimation
Alternating renewal process

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10.1111/sjos.12619Licence: CC BY

ArticleFinal published version, 1.91 MBLicence: CC BY

2 Citations
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State estimation for aoristic models
van Lieshout, M. N. M. & Markwitz, R. L., 24 Aug 2021, ArXiv.org, 16 p.
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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.",

keywords = "UT-Hybrid-D, Aoristic data, Criminological data, Marked temporal point process, Markov chain Monte Carlo methods, Markov point process state estimation, Alternating renewal process",

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note = "Funding Information: This research was funded by NWO, the Dutch Research Council (grant OCENW.KLEIN.068). We would additionally like to thank the reviewers, who significantly improved the quality of the work. Publisher Copyright: {\textcopyright} 2022 The Authors. Scandinavian Journal of Statistics published by John Wiley & Sons Ltd on behalf of The Board of the Foundation of the Scandinavian Journal of Statistics.",

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KW - UT-Hybrid-D

KW - Aoristic data

KW - Criminological data

KW - Marked temporal point process

KW - Markov chain Monte Carlo methods

KW - Markov point process state estimation

KW - Alternating renewal process

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M3 - Article

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VL - 50

SP - 1068

EP - 1089

JO - Scandinavian journal of statistics

JF - Scandinavian journal of statistics

IS - 3

ER -

State estimation for aoristic models

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Keywords

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State estimation for aoristic models

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