Institute of Mathematical Statistics Collections

Analyzing posteriors by the information inequality

Willem Kruijer and Aad van der Vaart

Full-text: Open access

Abstract

We give bounds on the concentration of (pseudo) posterior distributions, both for correct and misspecified models. The bounds are derived using the information inequality, entropy estimates, and empirical process methods.

Chapter information

Source
Banerjee, M., Bunea, F., Huang, J., Koltchinskii, V., and Maathuis, M. H., eds., From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner, (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2013) , 227-240

Dates
First available in Project Euclid: 8 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1362751190

Digital Object Identifier
doi:10.1214/12-IMSCOLL916

Mathematical Reviews number (MathSciNet)
MR3202636

Zentralblatt MATH identifier
1353.62029

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
posterior contraction, prior, Bayes

Rights
Copyright © 2010, Institute of Mathematical Statistics

Citation

Kruijer, Willem; van der Vaart, Aad. Analyzing posteriors by the information inequality. From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner, 227--240, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2013. doi:10.1214/12-IMSCOLL916. https://projecteuclid.org/euclid.imsc/1362751190


Export citation

References