Definition

In the MH algorithm we define the acceptance rate, $r$, as the threshold function that determines whether a state get’s accepted or not: $$r(x_{t-1},y)=\min\left\{1, \frac{\pi(y)T(x_{t-1}|y)}{\pi(x_{t-1})T(y|x_{t-1})} \right\}$$where $x_{t-1}$is the previous state, $y$ is the proposed state, and $T(\cdot|\cdot)$ is the proposal kernel.