Model Selection in Historical Research Using Approximate Bayesian Computation

Abstract

Formal Models and HistoryComputational 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 StudyThis 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.ImpactResults 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.

Analysing Cultural Frequency Data: Neutral Theory and Beyond

“…Archaeology and more generally cultural evolution have adopted this modelling paradigm and generative inference frameworks enjoy increasing popularity [e.g. 18,19,22,41,44,51,68,80,89]. They have been applied to questions as diverse as the inference of processes of cultural transmission [e.g.…”

“…18,19,44] and the estimation of growth rates and population sizes from cultural frequency data [e.g. 68], the investigation of the evolution of combat [80] or of the coevolution between genes and languages at a regional scale [e.g. 89].…”

Revealing patterns of cultural transmission from frequency data: equilibrium and non-equilibrium assumptions

“…genetics28293031, epidemiology32, biological anthropology33, history34, and archaeoology14151635) where likelihood functions cannot be determined and proper integration of the uncertainty associated with model assumptions is required. For each version of the model we determine the parameter values which are able to generate variant frequencies similar to the observed ones (i.e.…”

Generative inference for cultural evolution

“…In order to highlight the breadth of questions that can be addressed within a generative inference framework we outline two further applications, one to historical studies (a field with no strong tradition of quantitative treatments) and to linguistics. Rubio-Campillo [91] investigated the evolution of combat. He explored the validity of different versions of Lanchester's law predicting the causalities of two enemy forces engaged in a land battle, with a dataset comprising the total number of combatants and causalities from 1080 land battles spanning from the middle of the seventeenth to the beginning of the twentieth century.…”