Quantifying Artifacts over Time: Interval Estimation of a Poisson Distribution using the Jeffreys Prior

TL;DR

This paper introduces a simulation-based method to estimate artifact quantities over time using a Poisson model with Jeffreys prior, providing credible intervals with minimal assumptions, demonstrated on Roman coinage data.

Contribution

It presents a novel simulation approach for interval estimation of artifact counts over time using a Poisson model with Jeffreys prior, applicable with minimal assumptions.

Findings

Effective estimation of artifact abundance over time.

Credible intervals established with minimal assumptions.

Application to Roman coinage data demonstrates practical utility.

Abstract

This article presents a new method for estimating the amount of an artifact class in use at a given moment in the past from a random assemblage of archaeological finds. This method is based on the use of simulation, since an analytical solution is computationally impractical. Estimating the number of artifacts in use at any time $t$ is shown to follow a Poisson distribution, which allows for credible intervals to be established using the Jeffreys prior. This estimator works from minimal assumptions about the dating and duration of finds, as well as the intensity of collection, and is applied to coinage from four Roman-period sites excavated by the Roman Peasant Project (2009-2014). The result provides for an estimation of the abundance of material according to an interval of certainty.