Computation of a joint distribution for scan statistics with temporal-spatial structures

• Project/Area Number: 24500356
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: Kuriki Satoshi 統計数理研究所, 数理・推論研究系, 教授 (90195545)
• Co-Investigator(Renkei-kenkyūsha): TAKAHASHI Kunihiko 名古屋大学, 大学院・医学系研究科, 准教授 (50323259) ; HARA Hisayuki 同志社大学, 文化情報学部, 准教授 (40312988)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000); Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 空間疫学 / 多重性調整 / マルコフ性 / コーダルグラフ / スキャン統計量 / 多重比較 / 脳画像データ / ガウス確率場 / ジャンクション木

Outline of Final Research Achievements

By extracting the Markov structure from a set of random variables with temporal and spatial structures, we have established a fast computation method to evaluate the multiplicity-adjusted p-value of temporal-spatial scan statistics. In addition, we applied the proposed method to spatial epidemiology. We demonstrated the usefulness of the proposed method by analyzing several data. The basic idea is (i) to describe the geographic information (adjacent relationship) by a non-directed graph, and (ii) to extract the Markov structure via the chordal extension of the graph, and (iii) to evaluate the multiplicity-adjusted p-value by successive numerical integrations based on the Markov property. On Saturday 29th October 2016, at the Institute of Statistical Mathematics (Tachikawa, Tokyo), we organized the workshop "New Horizons of Applied Statistics".

Research Products

• [Journal Article] Recursive computation for evaluating the exact p-values of temporal and spatial scan statistics (2015)
  • Author(s): Kuriki, Satoshi; Takahashi, Kunihiko; Hara, Hisayuki
  • Journal Title: arXiv Volume: stat.CO
  • Open Access
• [Presentation] Recursive computation for evaluating the exact p-values of temporal and spatial scan statistics (2015)
  • Author(s): Kuriki, Satoshi; Takahashi, Kunihiko; Hara, Hisayuki
  • Organizer: 2015 IMS China
  • Place of Presentation: Kunming, China
  • Year and Date: 2015-07-01
  • Int'l Joint Research / Invited
• [Presentation] Exact calculation of multiplicity-adjusted p-values of scan statistics in spatial epidemiology (2014)
  • Author(s): S. Kuriki, K. Takahashi, H. Hara
  • Organizer: 7th International Conference of the ERCIM WG on Computational and Methodological Statistics (ERCIM 2014)
  • Place of Presentation: Pisa, Italy
  • Year and Date: 2014-12-07
• [Presentation] 地理情報のマルコフ化による空間疫学スキャン統計量のp値の正確計算
  • Author(s): 栗木哲
  • Organizer: 2012年度統計関連学会連合大会
  • Place of Presentation: 北海道大学（札幌）