α-Parallel prior and its properties

Junnichi Takeuchi, Shun Ichi Amari

研究成果: Contribution to journalArticle査読

16 被引用数 (Scopus)

抄録

It is known that the Jeffreys prior plays an important role in statistical inference. In this paper, we generalize the Jeffreys prior from the point of view of information geometry and introduce a one-parameter family of prior distributions, which we named the α-parallel priors. The α-parallel prior is defined as the parallel volume element with respect to the α-connection and coincides with the Jeffreys prior when α = 0. Further, we analyze asymptotic behavior of the various estimators such as the projected Bayes estimator (the estimator obtained by projecting the Bayes predictive density onto the original class of distributions) and the minimum description length (MDL) estimator, when the α-parallel prior is used. The difference of these estimators from maximum-likelihood estimator (MLE) due to the α-prior is shown to be regulated by an invariant vector field of the statistical model. Although the Jeffreys prior always exists, the existence of α-parallel prior with α ≠ 0 is not always guaranteed. Hence, we consider conditions for the existence of the a-parallel prior, elucidating the conjugate symmetry in a statistical model.

本文言語英語
ページ(範囲)1011-1023
ページ数13
ジャーナルIEEE Transactions on Information Theory
51
3
DOI
出版ステータス出版済み - 3 1 2005
外部発表はい

All Science Journal Classification (ASJC) codes

  • 電子工学および電気工学
  • 情報システム

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