CARMA random fields and their applications to large spatio-temporal data

• Project/Area Number: 17H01701
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• Research Institution: Tohoku University
• Principal Investigator: Matsuda Yasumasa 東北大学, 経済学研究科, 教授 (10301590)
• Co-Investigator(Kenkyū-buntansha): 栗原 考次 京都女子大学, 宗教・文化研究所, 教授 (20170087) ; 西井 龍映 長崎大学, 情報データ科学部, 教授 (40127684) ; 矢島 美寛 東北大学, 経済学研究科, 客員教授 (70134814)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Project Status: Completed (Fiscal Year 2022)
• Budget Amount: ¥12,090,000 (Direct Cost: ¥9,300,000、Indirect Cost: ¥2,790,000); Fiscal Year 2020: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000); Fiscal Year 2019: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000); Fiscal Year 2018: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2017: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
• Keywords: 空間データ / 時系列 / スペクトル / フーリエ変換 / Whittle推定 / 時空間データ / 時空間回帰モデル / spectral density / Bayesian kriging / spatial data / spatio temporal data / model selection / 多変量CARMAモデル / spectral density matrix / Whittle尤度 / Bayesian CARMA kriging / 時空間モデル / 非定常 / 欠損値 / ベイズ推定 / CARMAモデル / 節点 / Brownian sheet / スペクトル密度関数 / 観測誤差 / 局所定常モデル / 等方性 / 非定常性

Outline of Final Research Achievements

Our research achievements are summarized in the following 4 points. First one is to establish the estimation method for Spatial Continuous Auto-Regressive and Moving Average (spatial CARMA) models under the frequency domain together with the validation of consistency and asymptotic normality. The second one is the extension of spatial CARMA models from stationary models to non-stationary models whose parameters can depend on locations with the idea of locally stationary processes. Third one is the developments of spatial regression models by regarding spatio-temporal data as temporal obsrevations of functional spatial data. Applications to monthly COVID-19 new cases aggegated in prefectual levels clarifies that an increase of human mobility leads to an increase of COVID-19 new cases. Finally we conducted applications with spatio-temporal models in social science fields.

Academic Significance and Societal Importance of the Research Achievements

近年のICT技術の進歩は大規模な時空間データの収集を可能とし、社会科学分野においても蓄積されつつある。本研究は、大規模な時空間データのモデルを提案し、非定常モデルに拡張し、さらに空間データ回帰分析に拡張した。順番がつかない空間データをフーリエ変換することで近似的に独立とみなして推定を行うWhittle推定法を提案し、その良さを漸近理論を使って確立したところに、本研究の学術的な意義がある。さらにその実際の有効性を幸福度サーベイデータに応用して実証したところに、社会的な意義がある。

Research Products

• [Int'l Joint Research] Catholic University of Sacro Cuore(イタリア)
• [Int'l Joint Research] Catholic University of Sacro Cuore(イタリア)
• [Int'l Joint Research] Colorado State University(米国)
• [Int'l Joint Research] EM Lyon(フランス)
• [Int'l Joint Research] University of East Anglia(英国)
• [Int'l Joint Research] Catholic University of the Sacred Heart(イタリア)
• [Int'l Joint Research] London School of Economics(英国)
• [Journal Article] Discussion on Competition for Spatial Statistics for Large Datasets (2021)
  • Author(s): Yasumasa, Matsuda
  • Journal Title: Journal of Agricultural, Biological and Environmental Statistics Volume: 26 Issue: 4 Pages: 612-613
  • DOI: 10.1007/s13253-021-00463-1
  • Peer Reviewed
• [Journal Article] A threshold extension of spatial dynamic panel model with fixed effects (2021)
  • Author(s): Junyue, Wu. and Yasumasa, Matsuda
  • Journal Title: Journal of Spatial Econometrics Volume: 2 Issue: 1 Pages: 1-30
  • DOI: 10.1007/s43071-021-00008-1
  • Peer Reviewed
• [Journal Article] Lévy Driven CARMA Processes: Properties, Applications and Inference (2020)
  • Author(s): 松田 安昌
  • Journal Title: Journal of the Japan Statistical Society, Japanese Issue Volume: 49 Issue: 2 Pages: 265-280
  • DOI: 10.11329/jjssj.49.265
  • NAID: 130007949596
  • ISSN: 0389-5602, 2189-1478
  • Year and Date: 2020-03-30
  • Peer Reviewed / Open Access
• [Journal Article] Special feature:Spatial Statistics (2020)
  • Author(s): Yasumasa, Matsuda
  • Journal Title: Japanese Journal of Statstics and Data Science Volume: 3 Issue: 1 Pages: 103-105
  • DOI: 10.1007/s42081-020-00081-0
  • Peer Reviewed
• [Journal Article] Log-periodogram regression of two-dimensional intrinsic stationary ranodm fields (2020)
  • Author(s): Yoshihiro,Yajima and Yasumasa, Matsuda.
  • Journal Title: Japanese Journal of Statistics and Data Science Volume: 3 Issue: 1 Pages: 333-347
  • DOI: 10.1007/s42081-020-00078-9
  • Peer Reviewed
• [Journal Article] Evaluation of regional variations in healthcare utilization (2020)
  • Author(s): Ibuka Yoko、Matsuda Yasumasa、Shoji Keishi、Ishigaki Tsukasa
  • Journal Title: Japanese Journal of Statistics and Data Science Volume: 3 Issue: 1 Pages: 349-365
  • DOI: 10.1007/s42081-020-00082-z
  • NAID: 210000159752
  • Peer Reviewed
• [Journal Article] Spatial extension of generalized autoregressive conditional heteroskedasticity models (2020)
  • Author(s): Takaki Sato and Yasumasa Matsuda
  • Journal Title: Spatial Economic Analysis Volume: 16 Issue: 2 Pages: 1742-1780
  • DOI: 10.1080/17421772.2020.1742929
  • Peer Reviewed
• [Journal Article] Evaluation of Hotspot Cluster Detection using Spatial Scan Statistic based on Exact Counting (2019)
  • Author(s): Fumio Ishioka, Jun Kawahara, Masahiro Mizuta, Shin-ichi Minato, and Koji Kurihara
  • Journal Title: Japanese Journal of Statistics and Data Science Volume: 2 Issue: 1 Pages: 241-262
  • DOI: 10.1007/s42081-018-0030-6
  • NAID: 210000185707
  • Peer Reviewed / Open Access
• [Journal Article] A fast algorithm for combinatorial hotspot mining based on spatial scan statistic (2019)
  • Author(s): Minato, S., Kawahara, J., Ishioka,F., Mizuta, M. Kurihara, K.
  • Journal Title: Proceedings of the 2019 SIAM International Conference on Data Mining Volume: 1 Pages: 91-99
  • DOI: 10.1137/1.9781611975673.11
  • ISBN: 9781611975673
  • Peer Reviewed
• [Journal Article] Computer vision-based phenotyping for improvement of plant productivity: a machine learning perspective (2018)
  • Author(s): Mochida Keiichi、Koda Satoru、Inoue Komaki、Hirayama Takashi、Tanaka Shojiro、Nishii Ryuei、Melgani Farid
  • Journal Title: GigaScience Volume: 8 Issue: 1 Pages: 1-12
  • DOI: 10.1093/gigascience/giy153
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Strong model dependence in statistical analysis: goodness of fit is not enough for model choice (2018)
  • Author(s): Copas, J. & Eguchi, S.
  • Journal Title: Ann Inst Stat Math Volume: 印刷中 Issue: 01 Pages: 1-10
  • DOI: 10.1142/s2661335219500023
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Locally stationary spatio-temporal processes (2018)
  • Author(s): Matsuda, Y. and Yajima, Y.
  • Journal Title: apanese Journal of Statistics and Data Science Volume: 1 Issue: 1 Pages: 1-17
  • DOI: 10.1007/s42081-018-0003-9
  • NAID: 210000171296
  • Peer Reviewed / Open Access
• [Journal Article] Spatial and structured SVM for multilabel image classification (2018)
  • Author(s): S. Koda, A. Zeggada, F. Melgani and R. Nishii
  • Journal Title: IEEE Transactions on Geoscience and Remote Sensing Volume: 56 Pages: 5948-5960
  • DOI: 10.1109/tgrs.2018.2828862
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Statistical and Machine Learning approaches to predict gene regulatory networks from transcriptome datasets (2018)
  • Author(s): K. Mochida, S. Koda, K. Inoue and R. Nishii
  • Journal Title: Frontiers in Plant Science Volume: 9 Pages: 1-8
  • DOI: 10.3389/fpls.2018.01770
  • Peer Reviewed / Open Access
• [Journal Article] Spatial Autoregressive Conditional Heteroskedasticity Modles. (2018)
  • Author(s): Sato, T. and Matsuda, Y.
  • Journal Title: J.Japan Statist. Soc. Volume: 47 Pages: 221-236
  • Peer Reviewed
• [Journal Article] Continuous auto-regressive moving average random fields on Rn (2017)
  • Author(s): Brockwell Peter J.、Matsuda Yasumasa
  • Journal Title: J. Roy. Statist. Soc., Ser. B. Volume: 79 Issue: 3 Pages: 833-857
  • DOI: 10.1111/rssb.12197
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Diurnal Transcriptome and Gene Network Represented through Sparse Modeling in Brachypodium distachyon (2017)
  • Author(s): Koda S, Onda Y, Matsui H, Takahagi K, Uehara-Yamaguchi Y, Shimizu M, Inoue K, Yoshida T, Sakurai T, Honda H, Eguchi S, Nishii R and Mochida K
  • Journal Title: Front. Plant Sci Volume: 8 Pages: 2055-2055
  • DOI: 10.3389/fpls.2017.02055
  • Peer Reviewed / Open Access
• [Presentation] Spatial Dynamic Panel Models for Multilevel Dataset with Applications to Japanese Happiness Surveys (2021)
  • Author(s): Sato, T. and Matsuda, Y.
  • Organizer: The XV World Conference of Spatial Econometrics Association, Tokyo
• [Presentation] Functional regression models for spatio-temporal data (2021)
  • Author(s): Yasumasa Matsuda
  • Organizer: TRANSDISCIPLINARY ECONOMETRICS & DATA SCIENCE SEMINAR
  • Invited
• [Presentation] 社会科学における空間データ分析と幸福度研究への応用 (2020)
  • Author(s): 松田安昌
  • Organizer: 実験家のためのデータ駆動科学オンラインセミナー第5回「人間と社会のデータ科学」
  • Invited
• [Presentation] 多変量空間MAモデル (2020)
  • Author(s): 佐藤宇樹、松田安昌
  • Organizer: 統計関連学会連合大会
• [Presentation] 時空間ARMAモデル (2020)
  • Author(s): 松田安昌
  • Organizer: 東京大学応用統計ワークショップ
  • Invited
• [Presentation] Space time ARMA model (2020)
  • Author(s): Yasumasa Matsuda
  • Organizer: 科研費シンポジウムRecent Progress in Spatial and/or Spatio-temporal Data Analysis
• [Presentation] Bivariate Continuous ARMA random fields (2019)
  • Author(s): Yasumasa Matsuda
  • Organizer: Lilac International Conference on Application of Statistics
  • Int'l Joint Research / Invited
• [Presentation] Bivariate CARMA random fields (2019)
  • Author(s): 松田安昌
  • Organizer: 2019年度統計関連学会連合大会
  • Invited
• [Presentation] Introduction of spatial data models with applications to analysis of world happiness (2019)
  • Author(s): Yasumasa Matsuda
  • Organizer: Second Tohoku-UEA Research Symposium
  • Int'l Joint Research / Invited
• [Presentation] Bivariate CARMA random fields (2019)
  • Author(s): Yasumasa Matsuda
  • Organizer: 2nd ISM-UUlm Joint Workshop
  • Int'l Joint Research / Invited
• [Presentation] SAR(p)-GARCH(k, l) Models for High-Dimensional Financial Time Series (2019)
  • Author(s): Takaki Sato and Yasumasa Matsuda
  • Organizer: Korean Statistical Society
  • Int'l Joint Research / Invited
• [Presentation] SAR(p)-GARCH(k, l) Models for High-Dimensional Financial Time Series (2019)
  • Author(s): Takaki Sato and Yasumasa Matsuda
  • Organizer: The 12th World Conference of the spatial econometrics association
  • Int'l Joint Research
• [Presentation] SAR(p)-GARCH(k, l) Models for High-Dimensional Financial Time Series (2019)
  • Author(s): 佐藤宇樹, 松田安昌
  • Organizer: 2019年度統計関連学会連合大会
• [Presentation] Analysis of regional economic growth against crisis: US-Japan comparative study before-after Lehman's shock. (2019)
  • Author(s): G. Fitrianto, S. Tanaka and R. Nishii
  • Organizer: The 62th ISI World Statistics Congress
  • Int'l Joint Research
• [Presentation] 正定値行列の一般化平均 － 色認知空間上の楕円予測－ (2019)
  • Author(s): 江口 真透, 中本 尊元, 西井 龍映
  • Organizer: 2019年度統計関連学会連合大会
• [Presentation] Spatial perception for structured and unstructured data in topological data analysis (2019)
  • Author(s): Kitanishi, Y., Ishioka, F., Iizuka, M., Kurihara, K.
  • Organizer: 16th Conference of the International Federation of Classification Societies
  • Int'l Joint Research / Invited
• [Presentation] Cluster Detection Based on Restricted Hierarchical Structure for Large Scale Data (2019)
  • Author(s): Takemura, Y. Ishioka, F., Kurihara, K.
  • Organizer: Data Science, Statistics and Visualization 2019
  • Int'l Joint Research
• [Presentation] Cluster Detection Based on Restricted Hierarchical Structure for Large Scale Hotspot Detection for Epidemiological Data Analysis Using R Shiny (2019)
  • Author(s): Kajinishi, S., Ishioka, F., Kurihara, K.
  • Organizer: Data Science, Statistics and Visualization 2019
  • Int'l Joint Research
• [Presentation] On Gaussian Semiparametric Estimation of Two-Dimensional Intrinsically Stationary Random Fields (2019)
  • Author(s): Yoshihiro Yajima
  • Organizer: The 62th ISI World Statistics Congress
  • Int'l Joint Research
• [Presentation] Spatial GARCH Models. (2018)
  • Author(s): Sato, T. and Matsuda, Y.
  • Organizer: 12th World Conference of the spatial econometrics association, Vienna
  • Int'l Joint Research
• [Presentation] Spatial modeling of volatility matrices for high-dimensional financial time series. (2018)
  • Author(s): Matsuda, Y.
  • Organizer: Statistics and Data Science Workshop at King Abdullah Univ. of Science and Technology
  • Int'l Joint Research / Invited
• [Presentation] ビッグデータ時代の機械学習と統計手法 (2018)
  • Author(s): 西井龍映
  • Organizer: 電気情報通信学会 九州支部専門講習会
  • Invited
• [Presentation] Kullback-Leibler 情報量に基づく Alternating Direction Method of Multipliers による精度行列のスパース推定 (2018)
  • Author(s): 上田勇祐、西井龍映、江田智尊
  • Organizer: 統計関連学会連合大会
• [Presentation] Visualization of Cluster Detection based on Hierarchical Structure for Geospatial Data and its Application (2018)
  • Author(s): Ishioka, F., Kajitani, S., Kurihara, K.
  • Organizer: European Conference on Data Analysis, Paderborn, Germany
  • Int'l Joint Research / Invited
• [Presentation] Cluster detection for mutli-dimensional spatial data based on hierarchical structure (2018)
  • Author(s): Ishioka, F., Kurihara, K.
  • Organizer: COMPSTAT2018
  • Int'l Joint Research / Invited
• [Presentation] Statistical Gene Analysis And Contributions To Low-Carbon Society (2018)
  • Author(s): Satoru Koda, Ryuei Nishii,Keiichi Mochida, Yoshihiko Onda
  • Organizer: I2CNER Annual Symposium
• [Presentation] Statistical gene data analysis and applications to plant growth (2018)
  • Author(s): Satoru Koda, Yoshihiko Onda, Hidetoshi Matsui,Ryuei Nishii and Keiichi Mochida
  • Organizer: 共同研究集会
  • Int'l Joint Research
• [Presentation] Spatial Autoregressive Conditional Heteroscedasticity Models and Their Applications to Land Price Data in Tokyo. (2017)
  • Author(s): Sato, T. and Matsuda, Y.
  • Organizer: 11th World Conference of the Spatial Econometrics Association, June 13-15, 2017, Singapore Management University School of Economics, Singapore
  • Int'l Joint Research
• [Presentation] CARMA random fields on Rn (2017)
  • Author(s): Matsuda, Y.
  • Organizer: Lilac International Conference of Application on Statistics, in activity center of Harbin Institute of Technology from June 2nd to 5th, 2017
  • Int'l Joint Research / Invited
• [Presentation] Nonstationary extension of CARMA random fields. (2017)
  • Author(s): Matsuda, Y.
  • Organizer: Workshop on Levy processes and time series in honour of Peter Brockwell and Ross Maller. Ulm University, Ulm, Germany
  • Int'l Joint Research / Invited
• [Presentation] Spatio-temporal autoregressive conditional heteroskedasticity model. (2017)
  • Author(s): Sato, T. and Matsuda,
  • Organizer: 11th International Conference on Computational and Financial Econometrics. December 16-18, 2017, Senate House, University of London, UK.
  • Int'l Joint Research
• [Presentation] Spatio-temporal CARMA models in English Session: History and recent development of spatio-temporal statistics (2017)
  • Author(s): Matsuda, Y.
  • Organizer: 統計関連学会連合大会, 南山大学
• [Presentation] Feature Selection of Support Vector Regression Based on Information Theoretic Criteria (2017)
  • Author(s): 西井 龍映
  • Organizer: The SIAM Workshop on Parameter Space Dimension Reduction
  • Int'l Joint Research
• [Presentation] サポートベクター回帰における変数選択 (2017)
  • Author(s): 西井 龍映
  • Organizer: 統計関連学会連合大会
• [Presentation] Structured Support Vector Machine を用いた土地被覆画像のマルチラベル判別 (2017)
  • Author(s): 江田智尊, Abdallah Zeggada, Farid Melgani, 西井 龍映
  • Organizer: 日本分類学会第36回大会
• [Presentation] 太陽風が弱い地震の引き金であることの統計的検証 (2017)
  • Author(s): 西井 龍映
  • Organizer: 共同研究集会
• [Presentation] 異分野と統計学の相互貢献 (2017)
  • Author(s): 西井 龍映
  • Organizer: AIMaPワークショップ
• [Presentation] Cluster detection using spatial scan statistic and its new development in large-scale scanning. (2017)
  • Author(s): Ishioka, F. and Kurihara, K.
  • Organizer: 2017 Conference of the International Federation of Classification Societies, Tokyo, 2017.8.8.
  • Int'l Joint Research / Invited
• [Presentation] Statistical evaluation for spatial complexity based on echelon trees. (2017)
  • Author(s): Kurihara, K., Kajinishi, S. and Ishioka, F.
  • Organizer: 2017 Conference of the International Federation of Classification Societies, Tokyo, 2017.8.8.
  • Int'l Joint Research / Invited
• [Presentation] Evaluation of spatial cluster detection method based on all geographical linkage patterns. (2017)
  • Author(s): Ishioka, F., Kawahara, J., Kurihara, K.
  • Organizer: IASC-ARS2017 (The Conference of the Asian Regional Section of the International Association of Statistical Computing), Auckland, 2017.12.12.
  • Invited
• [Book] 時空間統計解析 (2019)
  • Author(s): 矢島美寛・田中潮
  • Total Pages: 256
  • Publisher: 共立出版株式会社
  • ISBN: 9784320113527
• [Funded Workshop] Recent Progress in Spatial and/or Spatio-temporal Data Analysis (2020)
• [Funded Workshop] Workshop on Recent Progress in Time Series: in honour of Peter Robinson (2019)
• [Funded Workshop] Data Science Workshop (2018)
• [Funded Workshop] Workshop on Econometric Analysis for Big Data (2018)
• [Funded Workshop] Workshop on spatial and spatio-temporal data analysis (2017)