# Questions tagged [hidden-markov-model]

Hidden Markov Models are used for modelling systems that are assumed to be Markov processes with hidden (i.e. unobserved) states.

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### Creating synthetic data for time series, Hidden Markov Model

Suppose that I have a task of classifying a time series. I decide to use Hidden Markov Model $\lambda(A, B, \pi)$, where $A$ is a transition matrix, $B$ is an emission probability, $\pi$ is an initial ...
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### Viterbi algorithm differs between digital communications and more general HMM?

I am self-learning Markov modelling, currently looking at simple examples of hidden markov models (HMMs) and more specifically, Viterbi's algorithm. I saw a few uses of Viterbi's algorithm in simple ...
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### HMM estimation (Baum-Welch) with 2 independent state variables

I'm trying to estimate a hidden Markov auto-regressive model with two independent state variables. You can think of one as determining the levels for the mean-reversion and the other determining the ...
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### Estimate the HMM parameters (2states), backward

I fitted a 2-states-HMM model last week, and generate a bunch of 1s and 0s, but I forgot to store its parameters (transition matrix). Now, I only got these 1s and 0s, how do I backward/reverse-...
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### Maximum Likelihood in the Markov Switching GARCH(1,1) Model

In the standard GARCH(1, 1) model with normal innovations: $$~\epsilon _{t}=\sigma _{t}z_{t}}$$ $$\sigma^2_t=\omega+\alpha\epsilon^2_{t-1}+\beta\sigma^2_{t-1}.$$ The (negative) log-...
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### Learning HMM parameters by counting?

In 8.4.3 of the book Speech and Language Processing: An introduction to natural language processing, the two matrices transition probabilities and emission probabilities can be learned by counting as ...
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### Compute likelihood of state given multiple observations?

I am trying to use Bayes formula to compute the likelihood of a given state given a collection of independent but not sequenced observations - knowing the priors and knowing the probabilities of being ...
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