The Annals of Applied Statistics

Estimating the number of casualties in the American Indian war: A Bayesian analysis using the power law distribution

Colin S. Gillespie

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Abstract

The American Indian War lasted over one hundred years, and is a major event in the history of North America. As expected, since the war commenced in late eighteenth century, casualty records surrounding this conflict contain numerous sources of error, such as rounding and counting. Additionally, while major battles such as the Battle of the Little Bighorn were recorded, many smaller skirmishes were completely omitted from the records. Over the last few decades, it has been observed that the number of casualties in major conflicts follows a power law distribution. This paper places this observation within the Bayesian paradigm, enabling modelling of different error sources, allowing inferences to be made about the overall casualty numbers in the American Indian War.

Article information

Source
Ann. Appl. Stat. Volume 11, Number 4 (2017), 2357-2374.

Dates
Received: September 2016
Revised: June 2017
First available in Project Euclid: 28 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1514430289

Digital Object Identifier
doi:10.1214/17-AOAS1082

Keywords
Power law Bayesian missing data long tailed

Citation

Gillespie, Colin S. Estimating the number of casualties in the American Indian war: A Bayesian analysis using the power law distribution. Ann. Appl. Stat. 11 (2017), no. 4, 2357--2374. doi:10.1214/17-AOAS1082. https://projecteuclid.org/euclid.aoas/1514430289


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Supplemental materials

  • MCMC Diagnostic plots. We provide additional diagnostic plots showing the convergence of the MCMC algorithms for the simulation and the American Indian war analyses.