Signal detection theory, uncertainty, and Poisson-like population codes

The juxtaposition of established signal detection theory models of perception and more recent claims about the encoding of uncertainty in perception is a rich source of confusion. Are the latter simply a rehash of the former? Here, we make an attempt to distinguish precisely between optimal and probabilistic computation. In optimal computation, the observer minimizes the expected cost under a posterior probability distribution. In probabilistic computation, the observer uses higher moments of the likelihood function of the stimulus on a trial-by-trial basis. Computation can be optimal without being probabilistic, and vice versa. Most signal detection theory models describe optimal computation. Behavioral data only provide evidence for a neural representation of uncertainty if they are best described by a model of probabilistic computation. We argue that single-neuron activity sometimes suffices for optimal computation, but never for probabilistic computation. A population code is needed instead. Not every population code is equally suitable, because nuisance parameters have to be marginalized out. This problem is solved by Poisson-like, but not by Gaussian variability. Finally, we build a dictionary between signal detection theory quantities and Poisson-like population quantities.