In this paper, we provide a Doob-style consistency theorem for
stationary models. Many applications involving Bayesian inference deal
with non independent and identically distributed data, in particular, with
stationary data. However, for such models, there is still a theoretical
gap to be filled regarding the asymptotic properties of Bayesian
procedures. The primary goal to be achieved is establishing consistency of
the sequence of posterior distributions. Here we provide an answer to the
problem. Bayesian methods have recently gained growing popularity in
economic modeling, thus implying the timeliness of the present paper.
Indeed, we secure Bayesian procedures against possible inconsistencies. No
results of such a generality are known up to now.The authors are grateful for the comments and suggestions of
two referees. Antonio Lijoi and Igor Prünster were supported by the
Italian Ministry of University and Research, grants 2006134525 and
2006133449, respectively. The research of Stephen G. Walker was funded by
an EPSRC Advanced Research Fellowship.