  This paper proposes a single form for statistical models that accommodates a
broad range of models, from ordinary least squares to agent-based
microsimulations. The definition makes it almost trivial to define morphisms to
transform and combine existing models to produce new models. It offers a
unified means of expressing and implementing methods that are typically given
disparate treatment in the literature, including transformations via
differentiable functions, Bayesian updating, multi-level and other types of
composed models, Markov chain Monte Carlo, and several other common procedures.
It especially offers benefit to simulation-type models, because of the value in
being able to build complex models from simple parts, easily calculate
robustness measures for simulation statistics and, where appropriate, test
hypotheses. Running examples will be given using Apophenia, an open-source
software library based on the model form and transformations described here.
