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 b road class of nonstationary signals. We show that under weak assumptio ns, the Bayesian optimal causal variance estimate shows asymmetric dyn amics: an abrupt increase in variance is more readily detectable than an abrupt decrease. By contrast, optimal adaptation to the mean displa ys symmetric dynamics when the variance is held fixed. After providing several empirical examples and a simple intuitive argument for our ma in result, we prove that optimal adaptation is asymmetrical in a broad class of model environments. This observation makes specific and fals ifiable predictions about the time course of adaptation in neurons pro bed with certain stimulus ensembles.