A Bayesian treatment of the German tank problem

TL;DR

This paper presents a Bayesian approach to estimating the total number of tanks in the German tank problem, allowing for uncertainty quantification and prior information incorporation, with illustrative examples and related problem surveys.

Contribution

It introduces a Bayesian methodology for the German tank problem, enhancing traditional estimation with probabilistic reasoning and prior knowledge integration.

Findings

Bayesian method quantifies uncertainty in population size estimates.

Incorporates prior beliefs into the estimation process.

Provides illustrative example and surveys related problems.

Abstract

The German tank problem has an interesting historical background and is an engaging problem of statistical estimation for the classroom. The objective is to estimate the size of a population of tanks inscribed with sequential serial numbers, from a random sample. In this tutorial article, we outline the Bayesian approach to the German tank problem, (i) whose solution assigns a probability to each tank population size, thereby quantifying uncertainty, and (ii) which provides an opportunity to incorporate prior information and/or beliefs about the tank population size into the solution. We illustrate with an example. Finally, we survey problems in other contexts that resemble the German tank problem.