PPubMed5 Jan 2016Cited 30×

Model Selection in Historical Research Using Approximate Bayesian Computation Model Selection in Historical Research Using ABC

Xavier Rubio-Campillo, John P. Hart

Abstract

Standard Bayesian inference updates a set of prior beliefs considering new evidence and a given likelihood function. Prior beliefs aggregate the existing knowledge of a given topic, and the degree of credibility of this knowledge. These beliefs are translated into parameters of the model. The possible values for each parameter receive an initial probability following a specific statistical distribution. The likelihood function is used to compute the probabilities of any given result considering the value of the input parameters. The updated knowledge (i.e. the the posterior distribution) is th

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ABC model selection shows a fatigue‑adjusted Lanchester model fits 300 years of battle data far better than classic linear or squared laws.

What’s new

i.Applied Approximate Bayesian Computation for model selection in historical research.
ii.Compared four variants of Lanchester's combat laws on a dataset of over 1,000 battles spanning 300 years.
iii.Identified decisive evidence favoring a new fatigue model over classical linear and squared models.
iv.Provided temporal parameter estimates (μ and σ) showing decreasing fighting efficiency over centuries.
v.Released the battle dataset and Python implementation as open‑source supplementary material.

How they did it

The study used the ABC rejection algorithm: parameters were sampled from prior distributions, each Lanchester variant was simulated, and the distance to the empirical battle data was computed. Runs with distances below a tolerance τ were kept, and Bayes Factors were calculated to select the best model and estimate posterior distributions of μ and σ.

What they found

Fatigue model decisively selected for all periods at τ = 0.0005; linear and squared models absent, logarithmic only present for the 17th‑century period.
Parameter μ mean values: 2.4 (1620‑1701), ~1.9 (1702‑1792 and 1793‑1860), 1.6 (1861‑1905).
σ shows larger dispersion in the oldest period; all models performed worse for the Napoleonic wars period.

Caveats

✕Historical battle data have small sample size and high variance.
✕The simple ABC rejection algorithm used is not the most efficient ABC method.
✕The fatigue model may still miss other dynamic factors influencing combat outcomes.
✕Pure Bayesian frameworks struggle with added complexity such as dynamic fighting values.

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