Sampling Hidden Markov Model

I am studying hidden Markov models, but I have some doubts about the inference phase. If I have any observations and I want to know the three parameters that characterize the model, can I use one of the MCMC techniques directly on the observations or do I have to first use the Viterbi algorithm or the forward-backward algorithm on the observations and then use one of MCMC techniques to know the three parameters?

The question is not clear to me. But if you want to sample from HMM, forward sampling can be used. Assuming $X$ are hidden states and $Y$ is observations, and we want to sample $N$ observations. The steps are:

• Sample from $X_1$
• Based on the sample we got of $X_1$ and $P(Y_1|X_1)$, sample $Y_1$
• Based on the sample we got of $X_1$ and $P(Y_2|X_1)$, sample $X_2$
• $\cdots$
• Hi, I apologize for the lack of clarity of the question. But the hidden states I can sample them through one of the mcmc techniques or I must necessarily use the forward sampling? – G.Carlà Jul 28 '17 at 15:34
• why MCMC? that is the part I do not understand. – Haitao Du Jul 28 '17 at 15:36
• I read a pdf file where it is written: Markov Chain Monte Carlo methods observe a series of observations, and iteratively costruct a markov chain such that it's equilibrium distribution. This is the pdf file site:isi.edu/~galstyan/courses/Presentations/… – G.Carlà Jul 28 '17 at 15:44
• @G.Carlà i think you confused with HMM learning and HMM sampling/inference. – Haitao Du Jul 28 '17 at 15:45
• You could kindly clarify the situation. Thanks in advance – G.Carlà Jul 28 '17 at 15:47