### 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 language | English |
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Title of host publication | 2012 International Symposium on Information Theory and Its Applications, ISITA 2012 |

Pages | 86-90 |

Number of pages | 5 |

Publication status | Published - 2012 |

Event | 2012 International Symposium on Information Theory and Its Applications, ISITA 2012 - Honolulu, HI Duration: 2012 Oct 28 → 2012 Oct 31 |

### Other

Other | 2012 International Symposium on Information Theory and Its Applications, ISITA 2012 |
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City | Honolulu, HI |

Period | 12/10/28 → 12/10/31 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science Applications
- Information Systems

### Cite this

*2012 International Symposium on Information Theory and Its Applications, ISITA 2012*(pp. 86-90). [6401057]

**Asymptotics of Bayesian estimation for nested models under misspecification.** / Miya, Nozomi; Suko, Tota; Yasuda, Goki; Matsushima, Toshiyasu.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2012 International Symposium on Information Theory and Its Applications, ISITA 2012.*, 6401057, pp. 86-90, 2012 International Symposium on Information Theory and Its Applications, ISITA 2012, Honolulu, HI, 12/10/28.

}

TY - GEN

T1 - Asymptotics of Bayesian estimation for nested models under misspecification

AU - Miya, Nozomi

AU - Suko, Tota

AU - Yasuda, Goki

AU - Matsushima, Toshiyasu

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84873564746&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873564746&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9784885522673

SP - 86

EP - 90

BT - 2012 International Symposium on Information Theory and Its Applications, ISITA 2012

ER -