  We propose a Bayesian inference approach for a class of latent Markov models.
These models are widely used for the analysis of longitudinal categorical data,
when the interest is in studying the evolution of an individual unobservable
characteristic. We consider, in particular, the basic latent Markov, which does
not account for individual covariates, and its version that includes such
covariates in the measurement model. The proposed inferential approach is based
on a system of priors formulated on a transformation of the initial and
transition probabilities of the latent Markov chain. This system of priors is
equivalent to one based on Dirichlet distributions. In order to draw samples
from the joint posterior distribution of the parameters and the number of
latent states, we implement a reversible jump algorithm which alternates moves
of Metropolis-Hastings type with moves of split/combine and birth/death types.
The proposed approach is illustrated through two applications based on
longitudinal datasets.
