 Gaussian simultaneity decision model

Let internal timing difference be $D=\delta +b+\epsilon$ with $\epsilon \sim N(0,s^2)$, and report simultaneous when $-h<D<h$. Standardizing the two interval bounds gives $P(\mathrm{same})=\Phi ((h-\delta -b)/s)-\Phi ((-h-\delta -b)/s)$. For positive $h,s$ and symmetric noise, this function peaks at $\delta =-b$. Its width reflects both noise and acceptance bounds, so it cannot identify a sensory window without additional assumptions.