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Markov Chain == Dynamic Bayesian Network?

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Continuing from the end of this thread:� I've been looking into Markov chains and understand some of the maths and probability side. However, I've noticed in many papers I've been reading that they mention Dynamic Bayesian Networks and sometimes use it synonymously with HMMs and other times as improvements of HMMs. Could someone clarify the relationship between DBNs and HMMs? I'd like to start getting some basic code done with HMMs but I'm not sure if I should be looking into DBNs instead, as they seem to be more efficient (from what I've read).

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