### Abstract

The prediction in Bayesian framework is extended from the point of view of renormalization group. For this purpose, we first make it clear that the advantages of Bayesian statistical inference can be understood by an adaptive property of a long-distance length scale. This suggests a close connection of Bayesian statistical inference to renormalization group. Next, we show that a cumulative entropic error can be rewritten as an effective action, which directly leads to a renormalization group equation in non-parametric Bayesian statistical inference. As a result, we introduce a scaling part to a prior distribution, and determine it so that we can obtain better prediction performance. We discuss how prediction performance improves, taking an example of a density estimation problem.

Original language | English |
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Pages (from-to) | 296-299 |

Number of pages | 4 |

Journal | Progress of Theoretical Physics Supplement |

Volume | 157 |

Publication status | Published - 2005 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Renormalization group in bayesian statistical inference.** / Aida, Toshiaki.

Research output: Contribution to journal › Article

*Progress of Theoretical Physics Supplement*, vol. 157, pp. 296-299.

}

TY - JOUR

T1 - Renormalization group in bayesian statistical inference

AU - Aida, Toshiaki

PY - 2005

Y1 - 2005

N2 - The prediction in Bayesian framework is extended from the point of view of renormalization group. For this purpose, we first make it clear that the advantages of Bayesian statistical inference can be understood by an adaptive property of a long-distance length scale. This suggests a close connection of Bayesian statistical inference to renormalization group. Next, we show that a cumulative entropic error can be rewritten as an effective action, which directly leads to a renormalization group equation in non-parametric Bayesian statistical inference. As a result, we introduce a scaling part to a prior distribution, and determine it so that we can obtain better prediction performance. We discuss how prediction performance improves, taking an example of a density estimation problem.

AB - The prediction in Bayesian framework is extended from the point of view of renormalization group. For this purpose, we first make it clear that the advantages of Bayesian statistical inference can be understood by an adaptive property of a long-distance length scale. This suggests a close connection of Bayesian statistical inference to renormalization group. Next, we show that a cumulative entropic error can be rewritten as an effective action, which directly leads to a renormalization group equation in non-parametric Bayesian statistical inference. As a result, we introduce a scaling part to a prior distribution, and determine it so that we can obtain better prediction performance. We discuss how prediction performance improves, taking an example of a density estimation problem.

UR - http://www.scopus.com/inward/record.url?scp=22144459407&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22144459407&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:22144459407

VL - 157

SP - 296

EP - 299

JO - Progress of Theoretical Physics Supplement

JF - Progress of Theoretical Physics Supplement

SN - 0375-9687

ER -