### 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.

Original language | English |
---|---|

Pages (from-to) | 2352-2360 |

Number of pages | 9 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E97A |

Issue number | 12 |

DOIs | |

Publication status | Published - 2014 Dec 1 |

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### Keywords

- A class of probabilistic models
- Bayesian inference
- Cumulative logarithmic loss
- Misspecification
- Sequential prediction

### ASJC Scopus subject areas

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

### Cite this

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E97A*(12), 2352-2360. https://doi.org/10.1587/transfun.E97.A.2352

**Asymptotics of Bayesian inference for a class of probabilistic models under misspecification.** / Miya, Nozomi; Suko, Tota; Yasuda, Goki; Matsushima, Toshiyasu.

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E97A, no. 12, pp. 2352-2360. https://doi.org/10.1587/transfun.E97.A.2352

}

TY - JOUR

T1 - Asymptotics of Bayesian inference for a class of probabilistic models under misspecification

AU - Miya, Nozomi

AU - Suko, Tota

AU - Yasuda, Goki

AU - Matsushima, Toshiyasu

PY - 2014/12/1

Y1 - 2014/12/1

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.

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.

KW - A class of probabilistic models

KW - Bayesian inference

KW - Cumulative logarithmic loss

KW - Misspecification

KW - Sequential prediction

UR - http://www.scopus.com/inward/record.url?scp=84924559820&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84924559820&partnerID=8YFLogxK

U2 - 10.1587/transfun.E97.A.2352

DO - 10.1587/transfun.E97.A.2352

M3 - Article

VL - E97A

SP - 2352

EP - 2360

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 12

ER -