IEICE TRANSACTIONS on Fundamentals
Asymptotics of Bayesian Inference for a Class of Probabilistic Models under Misspecification
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E97-A No.12 pp.2352-2360
- Publication Date
- 2014/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E97.A.2352
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Prediction
Authors
Nozomi MIYA
Waseda University
Tota SUKO
Waseda University
Goki YASUDA
Waseda University
Toshiyasu MATSUSHIMA
Waseda University
Keyword
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Nozomi MIYA, Tota SUKO, Goki YASUDA, Toshiyasu MATSUSHIMA, "Asymptotics of Bayesian Inference for a Class of Probabilistic Models under Misspecification" in IEICE TRANSACTIONS on Fundamentals,
vol. E97-A, no. 12, pp. 2352-2360, December 2014, doi: 10.1587/transfun.E97.A.2352.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E97.A.2352/_p
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@ARTICLE{e97-a_12_2352,
author={Nozomi MIYA, Tota SUKO, Goki YASUDA, Toshiyasu MATSUSHIMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Asymptotics of Bayesian Inference for a Class of Probabilistic Models under Misspecification},
year={2014},
volume={E97-A},
number={12},
pages={2352-2360},
abstract={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.},
keywords={},
doi={10.1587/transfun.E97.A.2352},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - Asymptotics of Bayesian Inference for a Class of Probabilistic Models under Misspecification
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2352
EP - 2360
AU - Nozomi MIYA
AU - Tota SUKO
AU - Goki YASUDA
AU - Toshiyasu MATSUSHIMA
PY - 2014
DO - 10.1587/transfun.E97.A.2352
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E97-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2014
AB - 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.
ER -
English
