Given a transition matrix, starting probability, means and covariances

Is it possible to predict the most likely observed sequence for a given state sequence using the above details? If yes, how?

Thanks in advance.


Yes; this is just the expected value with respect to $P(Y|M, S)$ where $Y$ is the observed sequence, $M$ represents the parameters of the HMM, and $S$ is the given state sequence. Since your state sequence is given, you don't even need the transition matrix or starting probabilities; we're only interested in the part of the model that generates the observations (probably a Gaussian given your description). So, assuming univariate observations:

$$P(Y|M,S) = \prod_i^N \mathbb{N}(y_i|\mu_{s_i}, \sigma_{s_i})$$

where $s_i$ is the state for observation $i$ in the sequence. As we know, the expected value of a Gaussian is just its mean value, so the most likely observed sequence Y is the sequence $\{\mu_{s_1}, ... , \mu_{s_N}\}$.


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