Distribution Characteristics of Bayesian Resampling Method in Multivariate Data and its Application

• Project/Area Number: 15K00051
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Yokohama City University
• Principal Investigator: Hashiguchi (Ono) Yoko 横浜市立大学, データサイエンス学部, 准教授 (60339140)
• Co-Investigator(Kenkyū-buntansha): 橋口 博樹 東京理科大学, 理学部第一部応用数学科, 教授 (50266920) ; 中川 重和 岡山理科大学, 総合情報学部, 教授 (90248203)
• Research Collaborator: Kobayashi Hidetsune
• Project Period (FY): 2015-04-01 – 2019-03-31
• Project Status: Completed (Fiscal Year 2018)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: ベイズ型リサンプリング法 / 統計量分布特性 / 自動証明 / 統計賞分布特性

Outline of Final Research Achievements

We compared the accuracy of Bootstrap method (BST), Parametric Bootstrap method (PBST), and Bayesian Bootstrap method (BBST) in hypothesis testing of the mean of the two normal populations. According to the simulation results, it is confirmed that the accuracy of PBST is higher than the other two methods.
We also attempted to apply the resampling method to the selection of certification policies in automated reasoning problems. We use the resampling method to narrow down the number of proposed rules and make it possible to reduce the number of rules to a realistic number. The use of statistical methods to eliminate new nonsense ideas, which have exploded in number and appearance, in automatic verification led to the start of a new study on statistical learning.

Academic Significance and Societal Importance of the Research Achievements

ブートストラップ法（BST法）は,遺伝子解析や分子系統樹の作成など，医療・生命分野に利用されており，今後更なる適用範囲の拡大が予測される手法である．しかし，リサンプリング法が内包する標本への過敏性を考慮し，ビッグデータへの適用を鑑みるならば，多変量データに関する統計量分布の問題を回避することは難しいと思われる．本研究において，BST 法の一般型とも言えるベイジアン型リサンプリング法を多変量データへ適用することにより，その研究成果から，多変量データを扱う上でのリサンプリング法適用上の問題点や，適用が難しい統計量などが明確に示されることが予想される．

Research Products

• [Journal Article] Estimation of the Variance for the Maximum Likelihood Estimates in Normal Mixture Models and Normal Hidden Markov Models (2011)
  • Author(s): Masanari Iida and Naoto Niki
  • Journal Title: Journal of the Japanese Society of Computational Statistics Volume: 24 Issue: 1 Pages: 39-66
  • DOI: 10.5183
  • NAID: 10030497169
  • ISSN: 0915-2350, 1881-1337
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Presentation] Holonomic properties and recurrence formula for the distribution of sample correlation coefficient (2018)
  • Author(s): Haruto Mura, Hiroki Hashiguchi, Shigekazu Nakagawa, Yoko Ono.
  • Organizer: Statistical Computing:Challenges and Opportunities in Data Science，Beijing，November 2018
  • Int'l Joint Research
• [Presentation] 楕円母集団下でのウィシャート行列の最大最小固有値の分布について (2017)
  • Author(s): 篠崎絢,橋口博樹,岩下登志也
  • Organizer: 日本計算機統計学会
• [Presentation] Bootstrapping Distribution on the Eigenvalues of Covariance Matrix (2016)
  • Author(s): Hiroki Hashiguchi
  • Organizer: The 4th Indtitute of Mathematical Statistics Asia Pacific Rim Meeting
  • Place of Presentation: The Chinese University of Hong Kong, Hong Kong
  • Year and Date: 2016-06-27
  • Int'l Joint Research
• [Presentation] Holonomic properties for the distribution of the sample correlation coefficient (2015)
  • Author(s): Hiroki Hashiguchi, Shigekazu Nakagawa and Yoko Ono
  • Organizer: IASC-ARS 2015
  • Place of Presentation: National University of Singapore
  • Year and Date: 2015-12-17
  • Int'l Joint Research