State estimation for aoristic models

TL;DR

This paper develops Bayesian methods for estimating the hidden points in aoristic data modeled as a marked point process, incorporating prior information and analyzing the influence of prior choices.

Contribution

It introduces a Bayesian framework for state estimation in aoristic models with Markov priors and renewal process marks, including derivation of the posterior and parameter estimation.

Findings

Derived the posterior distribution for the latent points.

Analyzed the influence of prior distributions on estimates.

Provided examples illustrating the estimation process.

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 modelled in terms of an alternating renewal process in equilibrium and the prior is a Markov point point process. We derive the posterior distribution, estimate its parameters and present some examples that illustrate the influence of the prior distribution.