 | Figure 2
Nature Neuroscience
- 9, 1432 - 1438 (2006)
Published online: 22 October 2006; | doi:10.1038/nn1790
Bayesian inference with probabilistic population codesWei Ji Ma, Jeffrey M Beck, Peter E Latham & Alexandre Pouget | | | | Figure 2. Inference with probabilistic population codes for Gaussian probability distributions and Poisson variability.
The left plots correspond to population codes for two cues, c
1 and c
2, related to the same variable s. Each of these encodes a probability distribution with a variance inversely proportional to the gains, g
1 and g
2, of the population codes (K is a constant depending on the width of the tuning curve and the number of neurons). Adding these two population codes leads to the output population activity shown on the right. This output also encodes a probability distribution with a variance inversely proportional to the gain. Because the gain of this code is g
1 + g
2, and g
1 and g
2 are inversely proportional to  1
2 and 2
2, respectively, the inverse variance of the output population code is the sum of the inverse variances associated with c
1 and c
2. This is precisely the variance expected from an optimal Bayesian inference (equation (3)). In other words, taking the sum of two population codes is equivalent to taking the product of their encoded distributions.
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