r/statistics • u/InternetRambo7 • 9d ago

Question [Question] What techniques or papers exist for adapting the Gaussian emission assumption in a Hidden Markov Model?

What techniques or papers exist for adapting the Gaussian emission assumption in a Hidden Markov Model to capture higher-order distributional properties, such as skewness and kurtosis, rather than just mean and variance? I’m especially interested in approaches that retain the HMM framework while allowing more flexible, non-Gaussian emission distributions.

Thanks!

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u/guesswho135 9d ago

Observations do not need to be generated from a Gaussian. The textbook example of sequential weather patterns uses a categorical distribution. STAN, JAGS, etc. will have no problem with non-Gaussian distributions, just specify whatever you want in the graphical model.

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u/ForeignAdvantage5198 7d ago

google search is indicated

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u/tandem-pandemonium 6d ago

Why can't you just use HMM and add log skew and log kurt as features? Not quite sure how this makes contextual sense in general, but if you want to do it, wouldn't this allow you to do it