Bayesian Approaches in Computational Neuroscience: Overview

Definition

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.

Detailed Description

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’ theorem. 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, for example, 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 sets but has in neuroscience...