Wonderful, wonderful paper! Excellent work!
I only have a few question for my understanding and curiosity (and perhaps that of other readers as well).
1) When you model spike generation as a Poisson process and the environment merely determines the rate, doesn't this already imply some sort of internal decision-making as to when exactly to place each individual spike? I.e., adding the exact saccade timing to the saccade direction (in some environments) which remains not fully predictable by the model? Did I understand this correctly?
2) Have you tried other processes than Poisson?
3) What were the reasons for the assumption that the 'hidden' spike generator acts independently of the environment in a 'default' or 'baseline' way that persists even when the environment changes? In tethered flight, we observe a decrease of the spike rate compared to a blank environment, when we, e.g., add a single stripe in closed loop, indicating that there is an interaction between the spontaneous rate and the one generated under the influence of the environment - or can your term become negative in some circumstances?