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I would like to detect repetitive patterns and deviations from these repetitions. I have historical data and can calculate probabilities for the transitions between my many states. I have researched into Markov chains somewhat and feel these could present the correct means of modelling my problem.

However I am confused by this and would appreciate some simple words which I have perhaps missed in the academic literature I have read to date.

Basically if I want to calculate the probability that my current set of events is repetitive so can I simple sum the transitions through my transition matrix and the closer I am to 1 the more certain I am the pattern is repetitive? Do I even need a Markov chains or just the transition matrix?



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This sounds like it might be hard in general. I think you want to express your transition matrix as a weighted sum of permutation matrices with a minimal number of weights providing good approximations. But given this, the coefficients of the permutation matrices would seem to provide a rough measure along these lines. –  Steve Huntsman Jul 25 '10 at 13:24
You might also consider the autocorrelation, see e.g. books.google.com/books?id=cB-ZZX2HcWQC&pg=PA31 –  Steve Huntsman Jul 25 '10 at 14:03
Thanks, I'll look into your suggestions –  David Jul 25 '10 at 20:13

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