Bayesian inference with probabilistic population codes *Nature Neuroscience*, Vol. 9, No. 11. (22 October 2006), pp. 1432-1438, doi:10.1038/nn1790 by Wei J. Ma, Jeffrey M. Beck, Peter E. Latham, Alexandre Pouget

@article{ma-et-al-2006, abstract = {Recent psychophysical experiments indicate that humans perform near-optimal Bayesian inference in a wide variety of tasks, ranging from cue integration to decision making to motor control. This implies that neurons both represent probability distributions and combine those distributions according to a close approximation to Bayes' rule. At first sight, it would seem that the high variability in the responses of cortical neurons would make it difficult to implement such optimal statistical inference in cortical circuits. We argue that, in fact, this variability implies that populations of neurons automatically represent probability distributions over the stimulus, a type of code we call probabilistic population codes. Moreover, we demonstrate that the Poisson-like variability observed in cortex reduces a broad class of Bayesian inference to simple linear combinations of populations of neural activity. These results hold for arbitrary probability distributions over the stimulus, for tuning curves of arbitrary shape and for realistic neuronal variability.}, author = {Ma, Wei J. and Beck, Jeffrey M. and Latham, Peter E. and Pouget, Alexandre}, day = {22}, doi = {10.1038/nn1790}, issn = {1097-6256}, journal = {Nature Neuroscience}, keywords = {ann, bayes, biology, cue-combination, math, model, population-coding, probability}, month = oct, number = {11}, pages = {1432--1438}, pmid = {17057707}, posted-at = {2011-11-04 08:10:41}, priority = {2}, publisher = {Nature Publishing Group}, title = {Bayesian inference with probabilistic population codes}, url = {http://dx.doi.org/10.1038/nn1790}, volume = {9}, year = {2006} }

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Ma, Beck, Latham and Pouget argue that optimal integration of population-coded probabilistic information can be achieved by simply adding the activities of neurons with identical receptive fields. The preconditions for this to hold are

- independent Poisson (or other "Poisson-like") noise in the input
- identically-shaped tuning curves in input neurons
- a point-to-point connection from neurons in different populations with identical receptive fields to the same output neuron.⇒

The model due to Ma et al. is simple and it requires no learning.⇒

According to Ma et al,'s work, computations in neurons doing multi-sensory integration should be additive or sub-additive. This is at odds with observed neurophysiology.⇒