#acceptance-ratio

Question 1: Single choice

Random-walk Metropolis–Hastings proposes $\theta^* \sim \mathcal{N}(\theta, \epsilon^2 I)$ from the current state $\theta$ and targets $p(\theta) \propto p^*(\theta)$ , where $p^*$ is unnormalised. With which probability is $\theta^*$ accepted?

$\min\left(1, \; p^*(\theta) / p^*(\theta^*)\right)$ 1
$\min\left(1, \; p^*(\theta^*) / p^*(\theta)\right)$ 2
$p(\theta^*)$ , which requires normalising $p^*$ first3
$\min\left(1, \; q(\theta^* \mid \theta)\, p^*(\theta^*) / p^*(\theta)\right)$ 4

Timed test