# Approximating Bernoulli distributions as Poisson distributions in analysis of neural data

I'm reading Analysis of Neural Data, by Kass et al (2014), where Kass argues that spike trains can be viewed as point processes (in chapter 19). Furthermore, he goes on to convert spike trains (that are events in continuous time) to discrete time by dividing the timeline into bins of equal size.

Now, let $Y_i$ be the numbers of spikes in bin $i$ of size $\Delta t$. Since $\Delta t$ is defined to be small, Kass arrives at the model $Y_i \sim \text{Bernoulli}(p_i)$. And since $p_i$ is also considered to be small, Kass approximates the Bernoulli distributions by Poisson distributions. Kass says that the main reason for this approximation is that this enables him to model the $Y_i$'s in the framework of a GLM since the Poisson regression model is part of the GLM methodology (see page 568).

But wouldn't you say that this last approximation is unnecessary? Why doesn't Kass just use logistic regression? Can anyone comment if Poisson regression is generally preferred in analysing neural data? And if so, why?

• Binomial converges to Poisson so such approximation is often used. Also don't you mean binomial rather then Bernoulli? – Tim Nov 11 '16 at 21:22
• @Tim in this case a sum over the Y_i's will indeed be a random variable, say Z, that has the binomial distribution. Then Z has an approximate Poisson distribution. But my issue with Kass is that he approximates the Y_i's as having Poisson distributions. Am I missing something? – harisf Nov 14 '16 at 21:41
• I can't see any reason for this. Bernoulli distribution is much simpler then Poisson, so I can't see any reason for such approximation (I didn't read the paper). Bernoulli distribution is also a part of GLM methodology (logistic regression) not less then Poisson regression. – Tim Nov 14 '16 at 21:47
• I agree with you. However there seems to be a tradition of approximating, as I've understood @HEITZ's answer. – harisf Nov 15 '16 at 8:05