We fit this model to a population of several dozen simultaneously-recorded macaque retinal ganglion cells (ON and OFF parasol cells), whose receptive fields completely covered several square degrees of visual space. \comment{, stimulated with spatially varying 120-Hz binary white noise.} We used a regularized maximum likelihood fitting procedure to determine functional connectivity, and found strong positive coupling between pairs of ON cells and pairs of OFF cells, and negative coupling between ON-OFF pairs, with the strongest coupling occurring between nearby pairs of cells. We also fit a version of the model in which coupling filters were eliminated, making the response of each model cell conditionally independent of its neighbors (i.e., dependent only on the stimulus and its own spiking history).

We then used the model to perform optimal Bayesian decoding (reconstruction) of a novel stimulus from a set of observed spike times. By comparing the performance of the uncoupled model and with that of the full (coupled) model, we assessed the importance of correlated spiking for encoding and decoding. We found that: (1) spatial receptive fields are significantly smaller under the coupled model, suggesting that some portion of the classical receptive field can be more accurately explained in terms of the spiking activity of nearby cells; (2) the coupled model provides significantly more accurate predictions of multi-neuronal spike trains, faithfully accounting for second and higher-order correlations; (3) model-based decoding was significantly more accurate than optimal linear decoding; and (4) stimuli can be decoded $\sim$10\% more accurately using reconstruction based on the coupled model compared to the uncoupled model. These results indicate that correlations in retinal spiking activity cannot be ignored without losing information.