  We propose two novel ways of introducing dependence among Poisson counts
through the use of latent variables in a three levels hierarchical model.
Marginal distributions of the random variables of interest are Poisson with
strict stationarity as special case. Order--$p$ dependence is described in
detail for a temporal sequence of random variables, however spatial or
spatio-temporal dependencies are also possible. A full Bayesian inference of
the models is described and performance of the models is illustrated with a
numerical analysis of maternal mortality in Mexico. Extensions to cope with
overdispersion are also discussed.
