Asymmetric dynamics in optimal variance adaptation

It has long been recognized that sensory systems adapt to their inputs. Here we formulate the problem of optimal variance estimation for a broad class of nonstationary signals. We show that under weak assumptions, the Bayesian optimal causal variance estimate shows asymmetric dynamics: an abrupt increase in variance is more readily detectable than an abrupt decrease. By contrast, optimal adaptation to the mean displays symmetric dynamics when the variance is held fixed. After providing several empirical examples and a simple intuitive argument for our main result, we prove that optimal adaptation is asymmetrical in a broad class of model environments. This observation makes specific and falsifiable predictions about the time course of adaptation in neurons probed with certain stimulus ensembles.