Bernoulli

  • Bernoulli
  • Volume 8, Number 4 (2002), 451-473.

Non-informative priors in the case of Gaussian long-memory processes

Anne Philippe and Judith Rousseau

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Abstract

In this paper, we consider an asymptotic Bayesian analysis for Gaussian processes with long memory. First, we determine the asymptotic expansion of the posterior density based on a normal approximation. This expansion leads to the construction of Bayesian confidence regions such as highest posterior density regions and to the determination of matching prior. Then, we generalize Clarke and Barron's result in the long-memory set-up. More precisely, we establish the asymptotic expansion of the Kullback-Leibler distance between the true density and the marginal density of the observations. As in the independent and identically distributed case, this result gives an asymptotic justification of Berger and Bernardo's algorithm to obtain reference priors.

Article information

Source
Bernoulli, Volume 8, Number 4 (2002), 451-473.

Dates
First available in Project Euclid: 7 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1078681379

Mathematical Reviews number (MathSciNet)
MR2003f:60071

Zentralblatt MATH identifier
1003.62026

Keywords
Kullback-Leibler distance Laplace expansion long memory matching prior reference prior spectral density

Citation

Philippe, Anne; Rousseau, Judith. Non-informative priors in the case of Gaussian long-memory processes. Bernoulli 8 (2002), no. 4, 451--473. https://projecteuclid.org/euclid.bj/1078681379


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