Probabilistic Population Codes for Bayesian Decision Making *Neuron*, Vol. 60, No. 6. (26 December 2008), pp. 1142-1152, doi:10.1016/j.neuron.2008.09.021 by Jeffrey M. Beck, Wei J. Ma, Roozbeh Kiani, et al.

@article{beck-et-al-2008, abstract = {When making a decision, one must first accumulate evidence, often over time, and then select the appropriate action. Here, we present a neural model of decision making that can perform both evidence accumulation and action selection optimally. More specifically, we show that, given a Poisson-like distribution of spike counts, biological neural networks can accumulate evidence without loss of information through linear integration of neural activity and can select the most likely action through attractor dynamics. This holds for arbitrary correlations, any tuning curves, continuous and discrete variables, and sensory evidence whose reliability varies over time. Our model predicts that the neurons in the lateral intraparietal cortex involved in evidence accumulation encode, on every trial, a probability distribution which predicts the animal's performance. We present experimental evidence consistent with this prediction and discuss other predictions applicable to more general settings.}, author = {Beck, Jeffrey M. and Ma, Wei J. and Kiani, Roozbeh and Hanks, Tim and Churchland, Anne K. and Roitman, Jamie and Shadlen, Michael N. and Latham, Peter E. and Pouget, Alexandre}, day = {26}, doi = {10.1016/j.neuron.2008.09.021}, issn = {1097-4199}, journal = {Neuron}, keywords = {ann, bayes, population-coding, probability}, month = dec, number = {6}, pages = {1142--1152}, pmcid = {PMC2742921}, pmid = {19109917}, posted-at = {2013-01-03 13:31:41}, priority = {2}, publisher = {Cell Press,}, title = {Probabilistic Population Codes for {B}ayesian Decision Making}, url = {http://dx.doi.org/10.1016/j.neuron.2008.09.021}, volume = {60}, year = {2008} }

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Beck et al. model build-up in the SC as accumulation of evidence from sensory input.⇒

Beck et al. argue that simply adding time point-to-time point responses of a population code will integrate the information optimally if the noise in the input is what they call *"Poisson-like"*.

That is somewhat expected as in a Poisson distribution with mean $\lambda$ the variance is $\lambda$ and the standard deviation is $\sqrt{\lambda}$ and adding population responses is equivalent to counting spikes over a longer period of time, thus increasing the mean of the distribution.⇒