An Overview of Bayesian Methods for Neural Spike Train Analysis

Table 1

Probability distributions for modeling neuronal spike count observations.

Distribution	Mean statistic	Variance	Note for observations 𝑌
Binomial (𝑝)	𝔼[𝑌]=𝑝	𝑝(1−𝑝)	𝑌∈{0,1}
Poisson (𝜆)	𝔼[𝑌]=𝜆	𝜆	𝑌≥0, 𝑌∈ℤ^+
Negative binomial (𝑟,𝑝)	𝔼[𝑌]=𝑝𝑟/(1−𝑝)	𝑝𝑟/(1−𝑝)^2	𝑌≥0, 𝑌∈ℤ^+ (overdispersed Poisson)
Skellam (𝜇1,𝜇2)	𝔼[𝑌]=𝜇1−𝜇2	𝜇1+𝜇2	𝑌∈ℤ (difference between two Poissons)