Solved – 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.

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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 $X_2$
  • $cdots$

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