Model Selection in Historical Research Using Approximate Bayesian Computation

Formal Models and History
Computational models are increasingly being used to study historical dynamics. This new trend, which could be named Model-Based History, makes use of recently published datasets and innovative quantitative methods to improve our understanding of past societies based on their written sources. The extensive use of formal models allows historians to re-evaluate hypotheses formulated decades ago and still subject to debate due to the lack of an adequate quantitative framework. The initiative has the potential to transform the discipline if it solves the challenges posed by the study of historical dynamics. These difficulties are based on the complexities of modelling social interaction, and the methodological issues raised by the evaluation of formal models against data with low sample size, high variance and strong fragmentation.
Case Study
This work examines an alternate approach to this evaluation based on a Bayesian-inspired model selection method. The validity of the classical Lanchester’s laws of combat is examined against a dataset comprising over a thousand battles spanning 300 years. Four variations of the basic equations are discussed, including the three most common formulations (linear, squared, and logarithmic) and a new variant introducing fatigue. Approximate Bayesian Computation is then used to infer both parameter values and model selection via Bayes Factors.
Impact
Results indicate decisive evidence favouring the new fatigue model. The interpretation of both parameter estimations and model selection provides new insights into the factors guiding the evolution of warfare. At a methodological level, the case study shows how model selection methods can be used to guide historical research through the comparison between existing hypotheses and empirical evidence.

形式化模型与历史学
计算模型正日益被用于研究历史动态过程。这一可被称为基于模型的历史学（Model-Based History）的新兴趋势，借助新近公开的数据集与创新性定量方法，基于文字史料深化我们对过往社会的认知。形式化模型的广泛应用，使得历史学家能够重新评估数十年前提出、却因缺乏合适的定量框架而至今仍存争议的假说。若能攻克历史动态研究所带来的诸多挑战，这一研究范式有望重塑历史学这一学科。这些挑战源于社会互动建模的复杂性，以及在样本量小、方差高且碎片化严重的数据上评估形式化模型时所引发的方法论难题。

案例研究
本研究基于贝叶斯启发的模型选择方法，探索了一种用于该评估的替代路径。本研究以跨越300年、涵盖千余场战役的数据集为基础，检验了经典兰彻斯特战斗法则（Lanchester’s laws of combat）的有效性。本文讨论了基础方程的四种变体，涵盖三种最常用的形式（线性、平方与对数形式），并提出了引入疲劳因素的全新变体。随后，研究采用近似贝叶斯计算（Approximate Bayesian Computation），通过贝叶斯因子（Bayes Factors）完成参数值推断与模型选择。

研究影响
研究结果显示，存在决定性证据支持引入疲劳因素的全新模型。对参数估计与模型选择结果的解读，为揭示推动战争演变的核心因素提供了全新视角。在方法论层面，本案例研究展示了如何通过现有假说与实证证据的比对，借助模型选择方法指导历史学研究。