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BAYESIAN CONSISTENCY FOR STATIONARY MODELS

Published online by Cambridge University Press:  25 April 2007

Antonio Lijoi ,
Igor Prünster  and
Stephen G. Walker
Antonio Lijoi
Affiliation:
University of Pavia and CNR-IMATI Milan
Igor Prünster
Affiliation:
University of Turin College Carlo Alberto, and ICER
Stephen G. Walker
Affiliation:
University of Kent
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Abstract

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.

Type
MISCELLANEA
Information
Econometric Theory , Volume 23 , Issue 4 , August 2007 , pp. 749 - 759
Copyright
© 2007 Cambridge University Press

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