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Inferring state of a process from imperfect observations
I am fairly lost on a problem where I'm trying to infer the state of a process given imperfect observations. I have a hunch that a Hidden Markov Model would be suitable, but don't quite know how to get started. Any input is appreciated! To avoid boring you with mundane details, I can describe my problem as follows:
I have built a machine that does research for me. The machine is always in one of two states: either it does research or it doesn't. Occasionally, when the machine does research, it emits a short beep. The machine never beeps when it does not do research.
The machine also has a light that indicates its state. The light is green when the machine does research, and it is red when the machine does not do research. Unfortunately, the light is a bit broken: sometimes it turns red even though the machine is doing research.
Over the past couple of weeks, I have noted down the time whenever the light changes (along with whether it changed from green to r