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Finite mixture and Markov-switching models generalize and, therefore, nestspecifications featuring only one component. While specifying priors in thetwo: the general (mixture) model and its special (single-component) case, itmay be desirable to ensure that the prior assumptions introduced into bothstructures are coherent in the sense that the prior distribution in the nestedmodel amounts to the conditional prior in the mixture model under relevantparametric restriction. The study provides the rudiments of setting coherentpriors in Bayesian univariate finite mixture and Markov-switching models. Oncesome primary results are delivered, we derive specific conditions for coherencein the case of three types of continuous priors commonly engaged in Bayesianmodeling: the normal, inverse gamma, and gamma distributions. Further, we studythe consequences of introducing additional constraints into the mixture model'sprior (such as the ones enforcing identifiability or some sort of regularity,e.g. second-order stationarity) on the coherence conditions. Finally, themethodology is illustrated through a discussion of setting coherent priors fora class of Markov-switching AR(2) models.

Coherent prior distributions in univariate finite mixture and Markov-switching models