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I have a pretty good handle on Hidden Markov Models, but I can't think of any examples of a Markov process with a directly observable state. Any examples?

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They are all over the place, albeit you sometimes need to make simplifying assumptions. You could model workplace participation as a Markov model. People can be in training, working, unemployed, on disability leave, maternity leave, not seeking work, retired. Retirement would be an absorbing state in this model. Individuals transition between the states, and you might want to know the overall breakdown in the society. Or you might want to model the transition matrix for different groups (say those with post-secondary training and those without).

You could model this as continuous time, or discretize. Say, consider the changes if any every three months, or whatever.

Another model could be Telecom subscription in a market with a fixed number of Telecoms. People enter the market, churn between Telecoms, and then possibly exit the system (maybe by dying, moving away, or switching technologies altogether).

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  • $\begingroup$ Thanks! Can you define "observable" for me though? I think that's where my confusion comes from. $\endgroup$ – infinitely_improbable Jul 26 '18 at 16:21
  • $\begingroup$ An observable state is one that the researcher can observe and note. In a hidden markov process, the state is inferred from other data that is observed. A physician might take measurements in a cancer patient at scheduled visits and infer from this that the patient had transitioned from one stage to another of the disease. That would be a hidden model. $\endgroup$ – Placidia Jul 26 '18 at 18:34

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