Abstract
Normative theories and statistical inference provide complementary approaches for the study of biological systems. A normative theory postulates that organisms have adapted to efficiently solve essential tasks, and proceeds to mathematically work out testable consequences of such optimality; parameters that maximize the hypothesized organismal function can be derived ab initio, without reference to experimental data. In contrast, statistical inference focuses on efficient utilization of data to learn model parameters, without reference to any a priori notion of biological function, utility, or fitness. Traditionally, these two approaches were developed independently and applied separately. Here we unify them in a coherent Bayesian framework that embeds a normative theory into a family of maximumentropy “optimization priors.” This family defines a smooth interpolation between a data-rich inference regime (characteristic of “bottom-up” statistical models), and a data-limited ab inito prediction regime (characteristic of “top-down” normative theory). We argue that the flexibility afforded by our framework is essential to address a number of fundamental challenges relating to inference and prediction in complex, high-dimensional biological problems.
