Using MCMC for Generation

I want to use MCMC to draw samples which are similar to the data I have. Let us consider the following example.

Data:
ABCPQ
PQRMN
PQRST
STXYZ
XYZAB

Let us say, I build a network out of this data. (Now, whether this would be a bayesian net or dynamic bayesian net is controversial. Because data may introduce the edges which form the cycles. I would want them to have a directed properties for the reasons mentioned below. May be this would be a dynamic bayes net, may be not, I am unsure). The net would something like this:

I have only counted the bigram frequencies, which might change in future, but the resultant graph would be some network with probabilities on the edges (which would sum up to one)

This graph is something I would call distribution X.

I am interested in

    a posterior P(y | X, e, h), 

    where (y belongs_to Y), and Y is a random variable representing the output,

        for the prior, we can assume Y is Normally distributed (at least for the time being)

    e is a set of external parameters. This is some information outside of the distribution which has strong correlations to some y belongs_to Y.

    h is a history of selection.

In simpler terms, I would want to select some node from the distribution based on some external information. Then, use this information with some (changed) external information to select the next node. Repeat this process n times, where n is the required range of the formed sequence. This iterating is exactly the markov chain.

So example generation would be: (after the burn-in time and when the sampler has learned)

    e = vowel 

    h = NULL

    y = generate(X, e, h) = A

    -------------------------
    e = consonant

    h = {A}

    y = generate(X, e, h) = B

    ---------------------------

My specific questions are:

 1. What package to use for MCMC in matlab that is suitable for this work?
 2. How to code the selection criterion for each selected sample, as in to accept or reject it? Are there any examples of such?
 3. What would be good resources for the MCMC coding? All I can find is the bayesian LR examples..