probability or statistics - How to implement Markov Chain Monte Carlo with built-in functions?

These days I'm trying to conduct a model sensitivity test which is heavily based on the Markov Chain Monte Carlo simulation approach.

And I find this 'MCMC' package that can perform Markov Chain Monte Carlo simulations.

However, I found this package doesn't use much of the built-in stochastic process functions.

Also, due to my very limited knowledge of stochastic processes, I'd like to get better understanding of MCMC via a more Mathematica way.

As such, I'm wondering if such MCMC simulations can be performed with higher-level built-in stochastic functions (e.g. RandomFunction, HiddenMarkovProcess)?

Update on 20160330:

Now I get better understanding of how the MCMC procedure works.

But, one thing I'm still not clear is how to generate the transition matrix needed by the DsicreteMarkovProcess in Mathematica.

Can someone provide a clue for this?

Note: Cross-posted at http://community.wolfram.com/groups/-/m/t/830659

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