#mixing

Question 1: Single choice

You run random-walk Metropolis–Hastings on the same posterior with a very small and with a very large proposal variance (compared with the scale of the posterior). What do the trace plots of a parameter typically look like?

Small: nearly all moves accepted but tiny, a slow drift; large: most rejected, long flat stretches1
Small: most moves rejected, long flat stretches; large: nearly all accepted, a slow drift2
Both look like well-mixed noise; only the acceptance rate differs between the two3
Small: well mixed; large: a slow drift, because big jumps overshoot the mode4

Timed test