Neural representation of probabilities for Bayesian inference

Abstract

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.

Confidence as Bayesian Probability: From Neural Origins to Behavior

“…Second, these theories have not yet been empirically validated. Because we know that behavior can in some cases take into account uncertainty (Ernst and Banks, 2002;Kö rding and Wolpert, 2004;Ma and Jazayeri, 2014;Maloney and Zhang, 2010), we know that some kind of probabilistic representation must exist, but it need not be a full probability distribution (e.g., Rich et al, 2015). One alternative to the idea of neural codes based on probability distributions are codes in which summary statistics, such as the mean and variance, are represented and computed independently.…”

Natural ITD statistics predict human auditory spatial perception

“…Previous reports have investigated the selectivity of midbrain neurons to the variability of spatial cues in the owl's auditory system (Cazettes et al 2014;Fischer and Peña 2017). These studies provided evidence of how sensory reliability could be represented (Fischer and Peña 2011;Rich et al 2015;Cazettes et al 2016) and integrated into an adaptive behavioral command (Cazettes et al 2018). Although the ITD statistics relevant to owls and humans differ based on the frequency range over which ITD is detected, and the coding of ITD cannot be assumed identical across species (Schnupp and Carr 2009), results of the present study support the hypothesis that specific ITD statistics, ITDrc and ITDv, determine human sound localization discriminability and novelty detection of acoustic spatial deviants.…”

Some Considerations on Mathematical Statistics for Dealing with Big Data from the Viewpoint of Educational Innovation

“…So in this subsection, the methods for mathematical statistics are discussed for big data based on neural science [6,7] and cognitive science [8].…”

“…Bayesian statistical inference describes how sensory and prior information can be combined optimally to guide behavior. The conclusions in [7] address what neural response properties allow a neural system to perform Bayesian prediction, i.e., predicting where a source will be in the near future given sensory information and prior assumptions. The work shows that the population vector decoder will perform Bayesian prediction when the receptive fields of the neurons encode the target dynamics with shifting receptive fields.…”