Probabilistic Population Codes

Currently there are two main working hypotheses that purport to answer the first of these questions: what do neural populations represent? The first (standard model) claims that populations encode the value of a stimulus. Whilst the second, more recent perspective, claims they encode a probability distribution over the possible values of a stimulus. The standard model can be caricatured in the following manner: Firstly we specify an encoding rule from stimulus x to neural rate ri. This will be a probabilistic mapping P (ri|x) due to neuronal noise. To decode1 we form P (x|r) and typically take a point estimate of the stimulus, one popular choice for which is the MAP estimate: x̂ = arg maxx P (x|r). In summary then, the standard model typically only considers a single source of uncertainty (arising from noisy neural activities) and only decodes a point estimate from the posterior. An example of this approach might be as follows: Let each neuron in the population have a bell shaped tuning curve: