A type of directed Graphical model (in particular a Dynamic Bayesian network). See here. I think in some interpretations, it's the same as a Bayesian network?

When modeling some Stochastic process, there are some variables in the graphical model that are a Markov process that gives the model dynamics.

A Hidden Markov Model (HMM) is a discrete-time finite-state homogenous Markov chain observed through a discrete-time memoryless invariant channel.

This is used, for instance, in Machine learning

STATISTICAL ANALYSIS OF HIDDEN MARKOV MODELS

https://www.wikiwand.com/en/Hidden_Markov_model

presentation

Inference

Forward algorithm

Find likelihood (prob of data, given parameters), computed from joint probability of data and last state.

Backward algorithm

Probability of data given initial state. Can also compute likelihood.

Combining forward $f$ and backward $b$: $P(x, h_i = k| \theta) = f_k (i) b_k (i)$

Viterbi algorithm

Learning

Baum-Welch algorithm, an EM algorithm