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 reevaluate 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. 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. 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.Funding for this work was provided by the SimulPast Consolider Ingenio project (CSD2010-00034) of the former Ministry for Science and Innovation of the Spanish Government and the European Research Council Advanced Grant EPNet (340828).Peer ReviewedPostprint (published version

Inferencia bayesiana para algunas leyes de Lanchester

Lanchester (1916) introdujo una serie de ecuaciones o leyes determinísticas para modelar los números de bajas en un combate sin refuerzos. Un inconveniente de estos modelos es que no son útiles ni para la inferencia ni para la predicción, ya que el resultado de una batalla viene determinado por los parámetros del sistema y los tamaños iniciales de cada ejército. Se han propuesto varias versiones estocásticas de las ecuaciones de Lanchester. En este artículo, se resumen algunos de estos modelos y se demuestra cómo utilizar la inferencia bayesiana para estimar los parámetros importantes dada la información a priori que proviene de batallas anteriores, simulaciones, etc. y dada una muestra de datos de un combate. Finalmente, se ilustran los métodos empleados con datos reales y simulados

Monk business: an example of the dynamics of organizations.

In this paper we present a dynamic model of an organization. It is shown that the quality of the members of the organization may cycle and that even if the organization promotes excellency, the organization may end up populated by mediocre agents only.Overlapping generations; Quanty organization;

Nation-Building Modeling and Resource Allocation Via Dynamic Programming

Dynamic programming is used in many military and industrial applications to solve sequential decision making problems. This research proposes the development of a model and approach to address the application of dynamic programming in nation-building modeling. Through the creation of component indices to capture the state of operational variables: Political, Military, Economic, Social, Infrastructure, and Information (PMESII), a functional form of a system of differential equations is developed to account for the interactions between the state indices and instruments of national power: Diplomatic, Informational, Military, and Economic (DIME). Solving this problem with dynamic programming provides an improved sequence which describes the application of DIME in a manner that minimizes an objective (i.e. cost, time) and allows the model to account for external factors such as an insurgent reaction to US policy. An application of the model is derived for Iraq to demonstrate the utility of the model and explore various aspects of the solution space. This modeling approach offers a potential significant capability when analyzing and planning for nation-building operations

The changing spatial distribution of economic activity across U.S. counties.

This paper studies the recent trends in the spatial distribution of economic activity in the United States. Using county-level employment data for 13 sector -which cover the entire economy- we apply semi-parametric techniques to estimate how agglometarion and congestion effects have changed between 1972 and 1992. Non-service sectors are found to be spreading out and moving away from centers of high economic activity to areas 20 to 60 kilometers away; service sectors, on the contrary, are increasingly concentrating in areas of high economic activity by attracting jobs from the surrounding 20 kilometers.Economic geography; Spatial externalities; U.S. counties;

Monk business: an example of the dynamics of organizations

In this paper we present a dynamic model of an organization. It is shown that the quality of the members of the organization may cycle and that even if the organization promotes excellency, the organization may end up populated by mediocre agents only

Quantifying War: From the Battle of Britain to Terrorism

Conflicts are central events in history, defining eras and the lives of their peoples. In this thesis, we demonstrate the use of three quantitative methods to three case studies from historical and conflict modelling. We begin with the application of the bootstrap to the Battle of Britain. The bootstrap allows us to answer counterfactual questions about the Battle of Britain, including the importance of targeting and tactical decisions on the final outcome of the battle. We quantify the final outcome using theoretical prior distributions associated with historical viewpoints. We next conduct a changepoint analysis of historical battle deaths. This requires the adaptation of changepoint analysis methods to heavy-tailed data, for which we formulate an algorithm before applying the algorithm to the case study. We find evidence for changes in the distribution of battle deaths through time. We finish with a case study of coalescence and fragmentation modelling, which has been proposed for insurgent-counter-insurgent conflict. We demonstrate that gel-shatter cycles are a previously unrecognised yet ubiquitous feature of such systems and discuss the robustness of these systems to perturbations in the underlying rules. Together, these case studies demonstrate the ability of modern methods to refine and deepen our understanding of historic conflicts

The changing spatial distribution of economic activity across U.S. counties

This paper studies the recent trends in the spatial distribution of economic activity in the United States. Using county-level employment data for 13 sector -which cover the entire economy- we apply semi-parametric techniques to estimate how agglometarion and congestion effects have changed between 1972 and 1992. Non-service sectors are found to be spreading out and moving away from centers of high economic activity to areas 20 to 60 kilometers away; service sectors, on the contrary, are increasingly concentrating in areas of high economic activity by attracting jobs from the surrounding 20 kilometers