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In empirical research involving latent Markov models, there is a tendency of research communities building up expertise on one particular class of such models, then shoehorning any given data set into that very model formulation. This talk attempts to overcome this myopia by offering a unifying view on what otherwise are often considered completely separate model classes --- from hidden Markov models to Cox processes --- thereby providing guidance as to how a latent Markov model formulation can be suitably tailored to the data at hand.