# Bayesian Approaches in Computational Neuroscience: Overview

**DOI:**https://doi.org/10.1007/978-1-4614-7320-6_778-2

## Detailed Description

Bayesian approaches in computational neuroscience rely on the properties of Bayesian statistics for performing inference over unknown variables given a data set generated through a stochastic process.

Given a set of observed data *d* _{ 1:n }, generated from a stochastic process *P*(*d* _{ 1:n }|*X*) where *X* is a set of unobserved variables, the posterior probability distribution of *X* is *P*(*X*|*d* _{ 1:n }) = *P*(*d* _{ 1:n }|*X*)*P*(*X*)/*P*(*d* _{ 1:n }) according to Bayes rule. *X* can be a set of fixed parameters as well as a series of variables of the same size as the data itself *X* _{ 1:n }.

Based on the posterior probability and a specified utility function, an estimate of *X* can be made that can be shown to be optimal, e.g., by minimizing the expected variance.

One common use of this principle within computational neuroscience is for inferring unobserved properties (hidden variables *X*) based on observed data, *d*. These techniques can be used for inference on any data set but has in neuroscience mostly been used for neurophysiological recordings, imaging, and behavioral data.

By their nature electrophysiological recordings are noisy and stochastic. Given the stochastic responses of neurons to stimuli, Bayesian methods can be used to infer the underlying stimuli or activation of the neurons, *X* _{ 1:n } (Electrophysiology Analysis, Bayesian).

For imaging data, an underlying neural activity *X* _{ 1:n }, e.g., firing rate at the level of individual columns of cortex, is assumed to give rise to measured responses *d* _{ 1:n }, e.g., the blood flow measured by fMRI, through a stochastic process. Inverting the process through the Bayesian inference allows for estimating the unknown neural activity (Imaging Analysis, Bayesian).

The ideas can also be useful for inferring properties about the behavior of individual human subjects, *X*, by the assumption of a stochastic process, *P*(*d* _{ 1:n }|*X*), through which characteristics of each individual subject leads to individual choices in an experimental task, *d* _{ 1:n } (Behavioural Analysis, Bayesian).

The abovementioned techniques all use Bayesian inference to infer underlying properties of recorded data but is essentially used as very effective tools for data analysis. An alternative line of research takes as the working hypothesis that the human brain has evolved to the point of itself approximating an ideal Bayesian observer (sometimes referred to colloquially as the Bayesian brain hypothesis). Accordingly this line of research compares human behavior to the output of such an ideal observer within, e.g., perceptual (Perception, Bayesian Models of) or cognitive tasks (Cognition, Bayesian Models of).

A related effort has proposed that the computations necessary to perform the steps of Bayesian inference can be done through populations of biological neurons (Bayesian Inference, Neural Models of).

There is a continued effort to translate ideas on Bayesian inference from machine learning and computer science into computational neuroscience, including recent advances in sampling techniques for inference.