I am new to the world of neuroscience and I would like to understand how come every paper in neuroscience that I read uses a Poisson process to model neural firing. Do I just have a biased sample of the papers I chose to read, or is it a biological fact that neural firing must follow a Poisson process? Why can't it follow, say, binomial, since it either spikes or it doesn't in a given time period. Also, where can I read more about how such a biological phenomena was discovered?
A small correction: I do appreciate the explanation on the difference between the two distributions but I am a statistician who is trying to understand my neuroscience colleagues and communication is key in statistics. I am just trying to comprehend why everyone in the field is using Poisson as opposed to using Binomial even when the bin size you decided on is sufficiently small. In other words, why would you not use Binomial, the bin size is so small that your data is only 0's and 1's (i.e. the spike happened or did not happen within this bin). Is it because Poisson counts discrete occurrences in a continuous domain? What discipline-specific papers would you recommend to read that justify/discuss/explain the continuous domain on neural spiking?