Metropolis-Hastings algorithm steps

The Metropolis-Hastings algorithm is the most general form of the MCMC processes. It is also the easiest to conceptualize and code. An example of pseudocode is given in the five-step process below. The Markov chain process is clearly shown in the code, where samples that are generated from the prior distribution are accepted as arising from the posterior distribution at the ratio of the probability of the joint... 

In the third step, the updated value(s), , are assigned as with probability equal to the minimum of r and 1 and, otherwise. Thus, the algorithm always accepts steps that increase the density and occasionally those that decrease it. The advantage to the asymmetric jumping rules in the Metropolis-Hastings algorithm is an increase in speed. 

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

By default, normMixMH samples from an independent candidate density and uses 1,000 steps in the Metropolis-Hastings algorithm. Therefore to sample using an independent iV(0,3 ) candidate density we type... 

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