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I'm building a HMM for some data where there are two different time delays. Specifically, I collect data in consecutive traces, such that the time delay between each data point within a trace is approximately fixed, and the time delay between each trace is approximately fixed, but the two are not equal.

If the time delay between traces was very large, the influence of the last state of one trace on the first state of the next would be negligible (exponential decay of state duration), and I could treat it as multiple observation sequences. That is not the case however - looking at the correlation of observation values between points, I find that the first and last points correlate, implying that indeed the time delay is short enough for information to be contained between the two.

So I was wondering - does anyone have a sense of how to develop a HMM where the time delay between integer time points changes? One way would be to take the time delay as the least common factor between the intra-trace and inter-trace delays, and somehow have observations 'skipped'. For example, if I make measurements every second, maybe the time delay between 'observations' would be 200 ms, but I would only actually make an observation every 5 time points. Is there a way to have a HMM with such 'unknown' points? Is there another way to approach the problem?

Thanks for any advice!

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# HMM with variable time delay

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