Figure 4. The target distribution is a half-half mixture of two normal distributions, one with mean 0 and standard deviation 0.5, the other with mean 2 and standard deviation 0.5.

This distribution is estimated using MCMC with the sliding move (see Figure 3). The starting value is 5.0. The window size (w) is a tuning parameter of the move. For each w value, the left panel shows the trace of the MCMC samples, while the right panel shows the histogram of the MCMC samples (discarding the first 20% samples as burn-in). When w is too small, the MCMC is doing baby steps and moves slowly to new states, as shown in the top panel. On the other hand, too bold moves with large w frequently get rejected and the MCMC is trapped in a state for too long. This can be seen in the middle image, with periods of stasis in the chain. In both cases, the algorithm is inefficient and the posterior distribution is not well estimated from the sample. In the last row, the inference appears to have converged.