  Chopin (2007) introduced a sequentially ordered hidden Markov model, for
which states are ordered according to their order of appearance, and claimed
that such a model is a re-parametrisation of a standard Markov model. This note
gives a formal proof that this equivalence holds in Bayesian terms, as both
formulations generate equivalent posterior distributions, but does not hold in
Frequentist terms, as both formulations generate incompatible likelihood
functions. Perhaps surprisingly, this shows that Bayesian re-parametrisation
and Frequentist re-parametrisation are not identical concepts.
