Analyzing posteriors by the information inequality

W. Kruijer; A. van der Vaart

doi:10.1214/12-IMSCOLL916

Analyzing posteriors by the information inequality

W. Kruijer, A. van der Vaart

PE&RC

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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.

Original language	English
Title of host publication	From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner
Editors	M. Banerjee, F. Bunea, J. Huang, V. Koltchinskii, M.H. Maathuis
Place of Publication	Beachwood, Ohio, USA
Publisher	Institute of Mathematical Statistics
Pages	227-240
ISBN (Print)	9780940600836
DOIs	https://doi.org/10.1214/12-IMSCOLL916
Publication status	Published - 2013

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10.1214/12-IMSCOLL916

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Kruijer, W., & van der Vaart, A. (2013). Analyzing posteriors by the information inequality. In M. Banerjee, F. Bunea, J. Huang, V. Koltchinskii, & M. H. Maathuis (Eds.), From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner (pp. 227-240). Institute of Mathematical Statistics. https://doi.org/10.1214/12-IMSCOLL916

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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.",

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Kruijer, W & van der Vaart, A 2013, Analyzing posteriors by the information inequality. in M Banerjee, F Bunea, J Huang, V Koltchinskii & MH Maathuis (eds), From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner. Institute of Mathematical Statistics, Beachwood, Ohio, USA, pp. 227-240. https://doi.org/10.1214/12-IMSCOLL916

Analyzing posteriors by the information inequality. / Kruijer, W.; van der Vaart, A.
From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner. ed. / M. Banerjee; F. Bunea; J. Huang; V. Koltchinskii; M.H. Maathuis. Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2013. p. 227-240.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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AU - Kruijer, W.

AU - van der Vaart, A.

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BT - From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner

A2 - Banerjee, M.

A2 - Bunea, F.

A2 - Huang, J.

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A2 - Maathuis, M.H.

PB - Institute of Mathematical Statistics

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Kruijer W, van der Vaart A. Analyzing posteriors by the information inequality. In Banerjee M, Bunea F, Huang J, Koltchinskii V, Maathuis MH, editors, 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. p. 227-240 doi: 10.1214/12-IMSCOLL916

Analyzing posteriors by the information inequality

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