Traceplot Metropolis-Hastings

When the Metropolis-Hastings algorithm is run blockwise and the parameters in different blocks are highly correlated, the candidate for a block won t be very far from the current value for that block. Because of this, the chain will move slowly around the parameter space very slowly. We observed this in Figure 6.15 and in the traceplots in Figure 6.16. The traceplots of the parameters of a blockwise Metropolis-Hastings chain look much more like those for a random-walk chain than those for an independent chain. 

Despite the fact that every candidate will be accepted, the Gibbs sampling chain moves through the parameter space similarly to the blockwise Metropolis-Hastings chain. This is shown in Figure 6.19 and the traceplots in Figure 6.20. 

The appearance of the traceplot of a Metropolis-Hastings chain depends on the type of candidate density used. 

Figure 8.1 The traceplots of /3o and 0i for 5000 steps of the Metropolis-Hastings algorithm.

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