Asymptotics of Bayesian estimation for nested models under misspecification

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We analyze the asymptotic properties of the cumulative logarithmic loss in the decision problem based on the Bayesian principle and explicitly identify the constant terms of the asymptotic equations as in the case of previous studies by Clarke and Barron and Gotoh et al. We assume that the set of models is given that identify a class of parameterized distributions, it has a nested structure and the source distribution is not contained in all the families of parameterized distributions that are identified by each model. The cumulative logarithmic loss is the sum of the logarithmic loss functions for each time decision -, e.g., the redundancy in the universal noiseless source coding.

Original languageEnglish
Title of host publication2012 International Symposium on Information Theory and Its Applications, ISITA 2012
Pages86-90
Number of pages5
Publication statusPublished - 2012 Dec 1
Event2012 International Symposium on Information Theory and Its Applications, ISITA 2012 - Honolulu, HI, United States
Duration: 2012 Oct 282012 Oct 31

Publication series

Name2012 International Symposium on Information Theory and Its Applications, ISITA 2012

Conference

Conference2012 International Symposium on Information Theory and Its Applications, ISITA 2012
CountryUnited States
CityHonolulu, HI
Period12/10/2812/10/31

ASJC Scopus subject areas

  • Computer Science Applications
  • Information Systems

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  • Cite this

    Miya, N., Suko, T., Yasuda, G., & Matsushima, T. (2012). Asymptotics of Bayesian estimation for nested models under misspecification. In 2012 International Symposium on Information Theory and Its Applications, ISITA 2012 (pp. 86-90). [6401057] (2012 International Symposium on Information Theory and Its Applications, ISITA 2012).