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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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

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

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

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Power law Bayesian missing data long tailed


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.

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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.