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Bayesian Consistency For Stationary Models

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  • Lijoi, Antonio
  • Prünster, Igor
  • Walker, Stephen G.

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.

Suggested Citation

  • Lijoi, Antonio & Prünster, Igor & Walker, Stephen G., 2007. "Bayesian Consistency For Stationary Models," Econometric Theory, Cambridge University Press, vol. 23(4), pages 749-759, August.
    • Handle: RePEc:cup:etheor:v:23:y:2007:i:04:p:749-759_07
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    Cited by:

    1. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    2. Kawakami, Hajime, 2023. "Doob’s consistency of a non-Bayesian updating process," Statistics & Probability Letters, Elsevier, vol. 203(C).

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