##The coupled generalized linear model (GLM)
The GLM model takes as input a bipolar object and produces spikes over time as output. Broadly speaking, the firing rate (or the likelihood of observing a spike in a given time bin) is modeled as a Poisson distribution where the conditional intensity depends on the input stimulus, the neuron's spike history and the spiking of nearby coupled neurons.
In the linear stage, each RGC spatially filters the bipolar mosaic signal over each temporal sample. The nonlinear stage produces the conditional intensity, usually by the exponential function (although sigmoid functions are sometimes used). A spike is generated in a time bin if the conditional intensity exceeds a random draw from a Poisson distribution.
y(t) ~ Poiss [ f(kx + hy + k0) ]
The firing rate y(t) is proportional to the Poisson distribution with intensity determined by a nonlinear function of the linear filter k over stimulus x as well as the coupling filters h over the spiking activity of nearby cells y with tonic component k0. See Shlens, 2014 for the mathematical details.
