A Hierarchical Bayesian Arms Race Model

There is a long history in the social sciences of building models to describe processes related to arms races. These include both theoretical models, such as the actionreaction Richardson model, and empirical models. In addition, there is a substantial literature on estimating parameters associated with these models given observations of military expenditures, or various proxies. Such methods should account for uncertainties in data, process understanding, and parameters. Relatively recent advances in hierarchical formulations for such models can be utilized to account for these sources of uncertainty and can incorporate scientific judgement in a probabilistically consistent manner. For example, the deterministic Richardson model can be used to motivate the structure of a hierarchical statistical model for a bilateral arms race. The purpose of this paper is to illustrate such an approach and apply it to previously studied arms races between Greece and Turkey, as well as between India and Pakistan.