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Assume you have a friend who lives far away and who you call daily to talk about what each of you did that day. Your friend has only three things he's interested in: walking in the park, shopping, and cleaning his apartment. The choice of what to do is determined exclusively by the weather on a given day. You have no definite information about the weather where your friend lives, but you know general trends. Based on what he tells you he did each day, you try to guess what the weather must have been like.
You believe that the weather operates as a discrete [[Markov chain]]. There are two states, "Rainy" and "Sunny", but you cannot observe them directly, that is, they are ''hidden'' from you. On each day, there is a certain chance that your friend will perform one of the following activities, depending on the weather: "walk", "shop", or "clean". Since your friend tells you about his activities, those are the ''observations''. The entire system is that of a
You know the general weather trends in the area and you know what your friend likes to do on average. In other words, the parameters of the HMM are known. In fact, you can write them down in the [[Python programming language]]:
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