Predictive Credible Region for Bayesian Diagnosis of a Hypothesis

• Yanagimoto Takemi

  Department of Industrial and Systems Engineering, Chuo University, 1-13-27, Kasuga Bunkyo-ku, Tokyo 112-8551, Japan.

• Ohnishi Toshio

  The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan.

抄録

A Bayesian method for diagnosing a hypothesis is proposed in terms of the optimum Bayesian predictor under the e-divergence loss. We introduce a predictive credible region as a modified version of a posterior credible region. The predictive credible region is closely related to the complement of the rejection region of the likelihood ratio test in the frequentist context. As an application we revisit the controversy regarding Lindley's paradox, and observe satisfactory performance of the proposed credible region in contrast to the Bayes factor. Another important application concerns a method for analyzing additional evidence when a hypothesis is once rejected.

収録刊行物

• ＪＯＵＲＮＡＬ　ＯＦ　ＴＨＥ　ＪＡＰＡＮ　ＳＴＡＴＩＳＴＩＣＡＬ　ＳＯＣＩＥＴＹ

  ＪＯＵＲＮＡＬ　ＯＦ　ＴＨＥ　ＪＡＰＡＮ　ＳＴＡＴＩＳＴＩＣＡＬ　ＳＯＣＩＥＴＹ 39 (1), 111-131, 2009

  日本統計学会

キーワード

• Bayes factor
• conjugate analysis
• <var>e</var>-divergence loss
• likelihood ratio test
• Lindley's paradox
• posterior credible region
• statistical test

詳細情報

• CRID: 1390001205287434368
• NII論文ID: 10025991948
• NII書誌ID: AA1105098X
• DOI: 10.14490/jjss.39.111
• ISSN: 13486365
• ISSN: 18822754
• MRID: 2571805
• NDL書誌ID: 10301208
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I10301208
• Web Site: https://www.jstage.jst.go.jp/article/jjss/39/1/39_1_111/_pdf
• 本文言語コード: en
• データソース種別:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• 抄録ライセンスフラグ: 使用不可