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 modelled 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.

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Scandinavian Journal of Statistics
State estimation for spatio-temporal point processes with applications to criminology

van Lieshout, M.-C., & Markwitz, R. (2023). State estimation for aoristic models. Scandinavian Journal of Statistics, 50, 1068–1089. doi:10.1111/sjos.12619