  Stimulus from the environment that guides behavior and informs decisions is
encoded in the firing rates of neural populations. Each neuron in the
populations, however, does not spike independently: spike events are correlated
from cell to cell. To what degree does this apparent redundancy impact the
accuracy with which decisions can be made, and the computations that are
required to optimally decide? We explore these questions for two illustrative
models of correlation among cells. Each model is statistically identical at the
level of pairs cells, but differs in higher-order statistics that describe the
simultaneous activity of larger cell groups. We find that the presence of
correlations can diminish the performance attained by an ideal decision maker
to either a small or large extent, depending on the nature of the higher-order
interactions. Moreover, while this optimal performance can in some cases be
obtained via the standard integration-to-bound operation, in others it requires
a nonlinear computation on incoming spikes. Overall, we conclude that a given
level of pairwise correlations--even when restricted to identical neural
populations--may not always indicate redundancies that diminish decision making
performance.
