We present a deterministic theory of the statistician based on two preferences: the estimation preference describes the statistician’s view of how well input data and models fit together and the prediction preference describes how well predictions and models fit together. Standard assumptions on these preferences, together with a consistency condition, imply that the estimation preference has an additively separable representation: the first term is the function representing the prediction preference, and the second term is a penalty function that depends only on the model. We relate our two- preference statistical theories to existing methods of classical and Bayesian estimation, identifying common features and show that, despite diGerences in terminology, many of these methods are equivalent. By optimizing over models, we derive the fit between input data and predictions from our statistical theories. We call these derived relationships empirical descriptions and identify necessary and suGicient conditions under which an empirical description is induced by some statistical theory. Finally, we characterize empirical descriptions that can be interpreted as consequences of a parametrized class of statistical theories of updating. The parametrization includes Bayesian, maximum likelihood and behavioral updating.