Figure 3.

Computation of the posterior distribution, and the Bayesian population vector (BPV), from responses of an optimally efficient encoding population. (a) Hypothetical prior distribution over the stimulus variable. (b) Optimal encoding population. Colored tick marks denote the preferred stimuli, s_n, of each neuron. Points represent (noisy) responses of each neuron to a particular stimulus value, with color indicating the preferred stimulus of the corresponding neuron. (c) The decoder convolves these responses with a linear filter (triplets of thin gray lines) with weights log h(m). The convolution output is exponentiated (boxes) and normalized by the sum over the decoder population, yielding an encoding of the posterior distribution, p(s|r⃗), whose integral against any function may then be approximated. As an example, the BPV is computed by summing these responses, weighted by their associated preferred stimulus values, to approximate the mean of the posterior, which is the Bayes least square estimate of the stimulus.