The Hidden Markov Model describes a hidden Markov Chain which at each step emits an observation with a probability that depends on the current state. We might model this process (with the assumption of sufficiently precious weather), and attempt to make inferences about the true state of the weather over time, the rate of change of the weather and how noisy our sensor is by using a Hidden Markov Model. Now, the weather *is* cloudy or clear, we could go and see which it was, so there is a “true” state, but we only have noisy observations on which to attempt to infer it. Consider a sensor which tells you whether it is cloudy or clear, but is wrong with some probability.
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