Multivariate Autoregressive Modeling and Granger Causality Analysis of Multiple Spike Trains

Table 1

𝜆𝑖(𝑡)	Exponential	Square
	exp(𝜇𝑖+𝜎𝑖𝑥𝑖(𝑡))	(𝜇𝑖+𝜎𝑖𝑥𝑖(𝑡))^2
𝜇𝑖	𝐸ln(^2[𝜆𝑖]𝐸[𝜆^2𝑖])	^432𝐸^2[𝜆𝑖]−𝐸[𝜆^2𝑖]2
𝜎𝑖	ln(𝐸[𝜆^2𝑖]𝐸^2[𝜆𝑖])	𝐸[𝜆𝑖]−32𝐸^2[𝜆𝑖]−𝐸[𝜆^2𝑖]2
𝑅𝐱(𝑖,𝑗)(𝑘)	ln(𝑅𝜆(𝑖,𝑗)(𝑘)/𝐸[𝜆𝑖]𝐸[𝜆𝑗])𝜎𝑖𝜎𝑗	−𝜇𝑖𝜇𝑗+(𝑅𝜆(𝑖,𝑗)(𝑘)−𝐸[𝜆𝑖]𝐸[𝜆𝑗])/2+𝜇^2𝑖𝜇^2𝑗𝜎𝑖𝜎𝑗