Bayesian Analysis

Universality of Bayesian Predictions

Alessio Sancetta

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Abstract

This paper studies the theoretical properties of Bayesian predictions and shows that under minimal conditions we can derive finite sample bounds for the loss incurred using Bayesian predictions under the Kullback-Leibler divergence. In particular, the concept of universality of predictions is discussed and universality is established for Bayesian predictions in a variety of settings. These include predictions under almost arbitrary loss functions, model averaging, predictions in a non-stationary environment and under model misspecification.

Article information

Source
Bayesian Anal., Volume 7, Number 1 (2012), 1-36.

Dates
First available in Project Euclid: 13 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1339616721

Digital Object Identifier
doi:10.1214/12-BA701

Mathematical Reviews number (MathSciNet)
MR2896708

Zentralblatt MATH identifier
1330.62151

Keywords
Bayesian methods loss function model averaging structural change universal prediction

Citation

Sancetta, Alessio. Universality of Bayesian Predictions. Bayesian Anal. 7 (2012), no. 1, 1--36. doi:10.1214/12-BA701. https://projecteuclid.org/euclid.ba/1339616721


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See also

  • Related item: Bertrand Clarke. Comment on Article by Sancetta. Bayesian Anal., Vol. 7, Iss. 1 (2012), 37-44.
  • Related item: Feng Liang. Comment on Article by Sancetta. Bayesian Anal., Vol. 7, Iss. 1 (2012), 45-46.
  • Related item: Alessio Sancetta. Rejoinder. Bayesian Anal., Vol. 7, Iss. 1 (2012), 47-50.