In Shane's answer to this question he suggests that Hidden Markov Models can be used more successfully than wavelets for anomaly / change detection (it was a bit unclear -the topic he was addressing is anomaly detection, although he uses the words "change detection")
I am not very familiar with Hidden Markov Models, but as I understand it, they require a known Markov process (all states and transition probabilities known) and for each state a known set of emission probabilities. The really interesting thing that can be done with these is that given a sequence of emissions one can find the most likely sequence of states that would have led to those emissions.
Assuming that I am understanding HMM correctly (please correct me if I am wrong), how is this used for anomaly detection? How would one determine the underlying Markov process to use and the emission probabilities to use an HMM for anomaly detection?