Asymptotics of Bayesian inference for a class of probabilistic models under misspecification

研究成果: Article

抄録

In this paper, sequential prediction is studied. The typical assumptions about the probabilistic model in sequential prediction are following two cases. One is the case that a certain probabilistic model is given and the parameters are unknown. The other is the case that not a certain probabilistic model but a class of probabilistic models is given and the parameters are unknown. If there exist some parameters and some models such that the distributions that are identified by them equal the source distribution, an assumed model or a class of models can represent the source distribution. This case is called that specifiable condition is satisfied. In this study, the decision based on the Bayesian principle is made for a class of probabilistic models (not for a certain probabilistic model). The case that specifiable condition is not satisfied is studied. Then, the asymptotic behaviors of the cumulative logarithmic loss for individual sequence in the sense of almost sure convergence and the expected loss, i.e. redundancy are analyzed and the constant terms of the asymptotic equations are identified.

元の言語English
ページ(範囲)2352-2360
ページ数9
ジャーナルIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
E97A
発行部数12
DOI
出版物ステータスPublished - 2014 12 1

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Misspecification
Bayesian inference
Probabilistic Model
Unknown
Constant term
Almost Sure Convergence
Prediction
Redundancy
Class
Statistical Models
Logarithmic
Asymptotic Behavior
Model

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics
  • Signal Processing

これを引用

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AU - Miya, Nozomi

AU - Suko, Tota

AU - Yasuda, Goki

AU - Matsushima, Toshiyasu

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N2 - In this paper, sequential prediction is studied. The typical assumptions about the probabilistic model in sequential prediction are following two cases. One is the case that a certain probabilistic model is given and the parameters are unknown. The other is the case that not a certain probabilistic model but a class of probabilistic models is given and the parameters are unknown. If there exist some parameters and some models such that the distributions that are identified by them equal the source distribution, an assumed model or a class of models can represent the source distribution. This case is called that specifiable condition is satisfied. In this study, the decision based on the Bayesian principle is made for a class of probabilistic models (not for a certain probabilistic model). The case that specifiable condition is not satisfied is studied. Then, the asymptotic behaviors of the cumulative logarithmic loss for individual sequence in the sense of almost sure convergence and the expected loss, i.e. redundancy are analyzed and the constant terms of the asymptotic equations are identified.

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KW - A class of probabilistic models

KW - Bayesian inference

KW - Cumulative logarithmic loss

KW - Misspecification

KW - Sequential prediction

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