Hidden Markov model

A Markov model where observations are dependent on a latent Markov process $X$

an HMM has an additional requirement that the outcome of $Y$ at time $t = t_{0}$ must be “influenced” exclusively by the outcome of $X$ at $t = t_{0}$ and that the outcomes of $X$ and $Y$ at $t < t_{0}$ must be conditionally independent of $Y$ at $t = t_{0}$ given $X$ at time $t = t_{0}$ .

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