Gaussian simultaneity decision model
= Gaussian simultaneity decision model
Let internal timing difference be $D=\delta+b+\varepsilon$ with $\varepsilon\sim N(0,s^2)$, 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.