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A Useful Algebraic System of Statistical Models

Ben Klemens


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, a software library based on the model form and transformations described here.


Ben Klemens. (2014). A Useful Algebraic System of Statistical Models. Center for Statistical Research & Methodology Research Report Series (Statistics #2014-06). U.S. Census Bureau. Available online at <>.

Source: U.S. Census Bureau, Center for Statistical Research & Methodology

Published online: July 24, 2014
Last revised: July 29, 2014


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Source: U.S. Census Bureau | Research and Methodology Directorate | Center for Statistical Research & Methodology | (301) 763-3215 (or |   Last Revised: August 12, 2014