# Questions tagged [hidden-markov-models]

This tag is for questions relating to "Hidden Markov model", a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobservable (i.e. hidden) states.

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### Hidden Markov Model of a stationary Markov chain is a stationary process.

Let $X=(X_i)_{i \ge 1}$ be an irreducible Markov chain started in its stationary distribution, and $Y=(Y_i)_{i \ge 1}$ be such that $Y_i=\phi(X_i)$ for an arbitrary function $\phi$. Note that $X$ is a ...
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### Hidden Markov Model

I am reading "Bayesian Reasoning And Machine Learning" and I'm doing exercise 23.3 (a) on p.490. Here's the exercise: Consider a HMM with 3 states $(M=3)$ and $2$ output symbols, with a ...
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### $\beta$-recursion calculation in matrix form in Hidden Markov Models

In the backward algorithm for inference in hidden markov models, how would we calculate $\beta$ in matrix form? In the answer to this question, I saw how to calculate $\alpha$ in matrix form, and now ...
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### Transformations of stochastic matrix that preserve equilibrium

I have a stochastic (Markov) matrix $W$. I would like to modify it, such that $W_{i,i}$ increases for all $i$ (and thus other elements decrease). However, I don't want to change the equilibrium ...
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Suppose $(Y, {\cal T}, \nu)$ is a measure space and $(X, {\cal S}, \mu_y)$ is a measure space for each fixed $y \in Y$; $\mu_y$ depends on $y$. What can we say about the ${\cal T}-{\cal B}$ ...
I try to understand the Viterbi algorithm for solving hidden Markov models. There is a pseudo-code of it in Wikipedia: In the row that marked in blue (starts with $T_2$) I don't understand: how does ...