Bayesian Analysis

Comment on article by Celeux et al.

Xiao-Li Meng and Florin Vaida

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Abstract

This discussion argues that any difficulty with DIC for missing data is due to DIC being intrinsically a large-sample measure and relying on point estimates. What is missing is not "missing data", but rather a set of coherent principles for DIC itself when the amount of data is not adequate to invoke quadratic approximation for a complex model. The non-uniqueness of data augmentation schemes for any observed-data model also argues for the importance of emphasizing inference "focus" in applying model complexity measures such as DIC. An attempt to bring in more Bayesian "flavor" into DIC also reveals that an insightful explanation is missing: neither pure Bayesian measure nor pure likelihood/sampling measure yield sensible results, but some hybrid ones do.

Article information

Source
Bayesian Anal. Volume 1, Number 4 (2006), 687-698.

Dates
First available in Project Euclid: 22 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1340370937

Digital Object Identifier
doi:10.1214/06-BA122D

Mathematical Reviews number (MathSciNet)
MR2282201

Zentralblatt MATH identifier
1331.62338

Keywords
Effective number of parameters Information criteria model selection missing data statistical principles

Citation

Meng, Xiao-Li; Vaida, Florin. Comment on article by Celeux et al. Bayesian Anal. 1 (2006), no. 4, 687--698. doi:10.1214/06-BA122D. https://projecteuclid.org/euclid.ba/1340370937


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See also

  • Related item: G. Celeux, F. Forbes, C. P. Robert, D. M. Titterington. Deviance information criteria for missing data models. Bayesian Anal., Vol. 1, Iss. 4 (2006), 651-673.