Neural representation of probabilities for Bayesian inference

Bayesian models are often successful in describing perception and behavior, but the neural representation of probabilities remains in question. There are several distinct proposals for the neural representation of probabilities, but they have not been directly compared in an example system. Here we consider three models: a non-uniform population code where the stimulus-driven activity and distribution of preferred stimuli in the population represent a likelihood function and a prior, respectively; the sampling hypothesis which proposes that the stimulus-driven activity over time represents a posterior probability and that the spontaneous activity represents a prior; and the class of models which propose that a population of neurons represents a posterior probability in a distributed code. It has been shown that the non-uniform population code model matches the representation of auditory space generated in the owl's external nucleus of the inferior colliculus (ICx). However, the alternative models have not been tested, nor have the three models been directly compared in any system. Here we tested the three models in the owl's ICx. We found that spontaneous firing rate and the average stimulus-driven response of these neurons were not consistent with predictions of the sampling hypothesis. We also found that neural activity in ICx under varying levels of sensory noise did not reflect a posterior probability. On the other hand, the responses of ICx neurons were consistent with the non-uniform population code model. We further show that Bayesian inference can be implemented in the non-uniform population code model using one spike per neuron when the population is large and is thus able to support the rapid inference that is necessary for sound localization.