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A hidden Markov model is a Markov chain for which the state is only partially observable. In other words, observations are related to the state of the system, but they are typically insufficient to precisely determine the state. Several well-known algorithms for hidden Markov models exist.

Related: Check memoryless property of a Markov chain I try to expand the verifyMarkovProperty function of the markovchain package to assess the Markov Property of transition matrices by assigning each unique realised state in the sequence of matrices an ID and testing the sequence of these IDs. However, I am not sure if my approach does make sense statistically.

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Definition. Let G be an acyclic causal graph (a graph in which each node appears only once along any path) with vertex set V and let P be a probability distribution over the vertices in V generated by G. G and P satisfy the Causal Markov Condition if every node X in V is independent of () given (). Motivation.

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