Consider a stochastic, binray, linear-nonlinear unit, with spiking output $s$, synaptic inputs $\mathbf x$, weights $\mathbf w$, and bias (threshold) $b$:
\begin{equation}\begin{aligned} s &\sim\operatorname{Bernoulli}[p = \Phi(a)] \\ a &= \mathbf w^\top \mathbf x + b, \end{aligned}\end{equation}where $\Phi(\cdot)$ is the cumulative distribution function of a standard normal distribution. Note that $\Phi(\cdot)$ can be rescaled to closely approximate the logistic sigmoid if desired. Assuming the mean $\mu$ and covariance $\Sigma$ of $\mathbf x$ are known, can we obtain the mean and covariance of $s$?
