A study on statistical inference and inference algorithm by using combinatorial algebra for big data analyses

2016 Fiscal Year Final Research Report

• Project/Area Number: 25330037
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Doshisha University (2016); Niigata University (2013-2015)
• Principal Investigator: Hara Hisayuki 同志社大学, 文化情報学部, 准教授 (40312988)
• Co-Investigator(Renkei-kenkyūsha): TAKEMURA Akimichi 滋賀大学, データサイエンス学部, 教授 (10171670) ; KURIKI Satoshi 統計数理研究所, 数理推論研究系, 教授 (90195545) ; NINOMIYA Yoshiyuki 九州大学, 数理学研究科, 准教授 (50343330) ; KOBAYASHI Kei 慶應義塾大学, 理工学部, 准教授 (90465922)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: グラフィカルモデル / 計算代数統計学 / 計算機統計学

Outline of Final Research Achievements

We studied parameter identifiability of directed Gaussian graphical models with one latent variable. In the scenario we consider, the latent variable is a confounder that forms a source node of the graph and is a parent to all other nodes, which correspond to the observed variables. We give some useful graphical conditions that is sufficient for the model to be identifiable.
We also studied the problem of the evaluation of multiplicity-adjusted p-value
of scan statistics in spatial epidemiology. We use some notions on graph theory and proposed an efficient algorithm to compute multiplicity-adjusted p-value of the exact distribution of scan statistics. We also implemented the proposed algorithm and confirm the usefulness of it through some real data examples.

Free Research Field

数理統計学