MCMC sampler comparator

What you are seeing: three different random-walk algorithms trying to sample from the same probability density $\pi(x, y)$. The grey shading on the left is the density itself (darker = higher probability). Each colored trail is one sampler laying down points: it tries to walk in a way that, in the long run, spends time at each $(x, y)$ in proportion to $\pi$.

A "good" sampler explores the whole region quickly and decorrelates; a "bad" sampler gets stuck. The right panels are live trace plots of the $x$ coordinate of each chain, plus its acceptance rate and effective sample size $N_\text{eff}$. Switch the target to the banana or the funnel to see HMC pull ahead; switch to the mixture to see samplers getting trapped in one mode.