Neural scaling laws for an uncertain world

Autonomous neural systems must efficiently process information in a wide range of novel environments, which may have very different statistical properties. We consider the problem of how to optimally distribute receptors along a one-dimensional continuum consistent with the following design principles. First, neural representations of the world should obey a neural uncertainty principle---making as few assumptions as possible about the statistical structure of the world. Second, neural representations should convey, as much as possible, equivalent information about environments with different statistics. The results of these arguments resemble the structure of the visual system and provide a natural explanation of the behavioral Weber-Fechner law, a foundational result in psychology. Because the derivation is extremely general, this suggests that similar scaling relationships should be observed not only in sensory continua, but also in neural representations of ``cognitive' one-dimensional quantities such as time or numerosity

STOCHASTIC TECHNOLOGY, RISK PREFERENCES, AND THE USE OF POLLUTING INPUTS

We investigate the comparative static effects of environmental and agricultural policies on pesticide and fertilizer use. Since such effects depend on technology and risk preference parameters, we estimate these from a panel data set of Illinois farms. Generalized method of moments is used on a set of nonlinear first order conditions.Environmental Economics and Policy,