Concordance and Covariance Functions for Environmental Modelling

The main goal of this project is to consolidate a productive and recognized working team and to enhance the cooperation among them in Chile, Brazil and France in the area of spatial statistics with applications in environmental and social sciences, including the construction of concordance measures that can be used to validate new methodologies to measure the poverty, and the estimation of covariance functions that characterize the spatial correlation of variables used to measure the atmospheric pollution.

Goals

There are three main topics to be developed during the period of time of this project

• Topic 1: Extension of the concordance to the multivariate case.
• Topic 2: Concordance analysis for spatial data.
• Topic 3: Asymptotics for the ML estimator of spatial processes under fixed domain.

Team

• From France:
  • Francois Bachoc and Jean-Michel Loubes, Institut de Mathematiques de Toulouse, Universite Paul Sabatier.
  • Didier Rulliére, Institut de Science Financiere et d’Assurances (ISFA), Université de Lyon.
• From Brazil:
  • Mario De Castro, Instituto de Ciencias Matematicas e de Computacao, Universidade de Sao Paulo (USP).
  • Filidor Vilca, Departamento de Estatistica, Universidade Estadual de Campinas (UNICAMP).
  • Fernanda De Bastiani, Departamento de Estatistica. Centro de Ciencias Exatas e da Natureza, Universidade Federal de Pernambuco (UFPE).
• From Chile:
  • Ronny Vallejos and Felipe Osorio, Departamento de Matematica, Universidad Tecnica Federico Santa Maria.
  • Manuel Galea, Departamento de Estadistica, Pontificia Universidad Catolica de Chile.
  • Moreno Bevilacqua, Facultad de Ingenieria y Ciencias, Universidad Adolfo Ibanez, Vina del Mar.

Publications

• Acosta, J., Alegria, A., Osorio, F., Vallejos, R. (2021). Assessing the effective sample size for large spatial datasets: A block likelihood approach. Computational Statistics and Data Analysis 162, 107282. doi: 10.1016/j.csda.2021.107282.
• Acosta, J., Vallejos, R., Gomez, J. (2022). Correlation integral for stationary Gaussian time series. (submitted)
• Bachoc, F., Durrande, N., Rulliere, D. Chevalier C. (2022). Properties and comparison of some kriging sub-model aggregation methods. Mathematical Geosciences 54, 941-977. doi: 10.1007/s11004-021-09986-2
• Bevilacqua, M., Caamaño, C., Arellano-Valle, R.B., Gomez C. (2022). A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers. Test 31, 644-674. doi: 10.1007/s11749-021-00797-5
• Bevilacqua, M., Caamaño, C., Porcu, E. (2022). Unifying compactly supported and Matern covariance functions in spatial statistics. Journal of Multivariate Analysis 189, 104949. doi: 10.1016/j.jmva.2022.104949
• Blasi, F., Caamaño, C., Bevilacqua, M., Furrer, R. (2022). A selective view of climatological data and likelihood estimation. Spatial Statistics 50, 100596. doi: 10.1016/j.spasta.2022.100596
• De Castro, M., Galea, M. (2021). Bayesian inference for the pairwise probability of agreement using data from several measurement systems. Quality Engineering 33, 571-580. doi: 10.1080/08982112.2021.1931317
• Faouzi, T., Porcu, E., Bevilacqua, M. (2020). Space-time estimation and prediction under infill asymptotics with compactly supported covariance functions. Statistica Sinica 32, 1187-1203. doi: 10.5705/ss.202020.0010
• Morales-Oñate, V., Crudu, F., Bevilacqua, M. (2021). Blockwise Euclidean likelihood for spatio-temporal covariance models. Econometrics and Statistics 20, 176-201. doi: 10.1016/j.ecosta.2021.01.001
• Osorio, F., Galea, M. (2022+). Agreement assessment between two measurement systems using robust P-splines (working paper).
• Osorio, F., Vallejos, R., Barraza, W., Ojeda, S.M., Landi, M.A. (2022). Statistical estimation of the structural similarity index for image quality assessment. Signal, Image and Video Processing 16, 1035-1042. doi: 10.1007/s11760-021-02051-9.
• Papaterra, M., Ojeda, S., Landi, M., Vallejos, R. (2021). Strategy for selecting a quality index for images. International Journal of Computer Information Systems and Industrial Management Applications 13, 348-363. PDF
• Perez, J., Acosta. J., Vallejos, R. (2022). Assessing the estimation of nearly singular covariance matrices for modelling spatial variables. (submitted)
• Uribe-Opazo, M., De Bastiani, F., Galea, M., Schemmer, R.C., Assumpcao, R.A.B. (2021). Influence diagnostics on a reparameterized t-Student spatial linear model. Spatial Statistics 41, 100481. doi: 10.1016/j.spasta.2020.100481
• Vallejos, R., Acosta, J. (2021). Effective sample size for multivariate spatial processes with an application to soil contamination. Natural Resource Modeling 34, e12322. doi: 10.1111/nrm.12322
• Vallejos, R., Acosta, J., Osorio, F. (2022+). Comparing two spatial variables with the probability of agreement (working paper).
• Vallejos, R., Perez, J., Ellison, A.M., Richardson, A.D. (2020). A spatial concordance correlation coefficient with an application to image analysis. Spatial Statistics 40, 100405. doi: 10.1016/j.spasta.2019.100405.
• Vidal, G., Yuz, J., Vallejos, R., Osorio, F. (2022). Point-process modeling and divergence measures applied to the characterization of passenger flow patterns of a metro system. IEEE Access 10, 26529-26540. doi: 10.1109/ACCESS.2022.3156078

PhD students

• Eloy Alvarado, PhD student in Statistics. Universidad de Valparaíso, Chile.
• Isaac Cortés, PhD student in Statistics. Instituto de Ciencias Matemáticas e de Computacao, Universidade de Sao Paulo, Brazil.
• John Gómez, PhD student in Mathematics. Consorcio PUCV-UTFSM-UV, Chile.
• Juan Carlos Saavedra, D.Sc. in Statistics. Universidad de Valparaíso, Chile. Thesis: Influence Diagnostics in Gaussian Spatio-Temporal Linear Models with Separable Covariance.

Activities

• 2020:
  • July 07: First organizational meeting.
  • July 21: Webinar given by Felipe Osorio, entitled “Assessment of local influence for the analysis of agreement”. [Slides]
  • July 28: Webinar given by Mario de Castro, entitled “Probability of agreement”. [Slides]
  • August 4: Webinar given by Ronny Vallejos, entitled “Assessing the concordance between two georeferenced variables”. [Slides]
  • August 25: Webinar given by Francois Bachoc, entitled “Asymptotic results for cross validation estimation of covariance parameters of Gaussian processes”. [Slides]
• 2022:
  • March 28 - April 02: Meeting: “Recent advances in the analysis of concordance”, ICMC-USP, Brazil
    • April 01: Talk by Felipe Osorio, “A robust estimate of the probability of agreement between two measurement systems using P-splines” [Abstract].
    • April 01: Talk by Ronny Vallejos, “Concordance analysis for georeferenced variables” [Abstract].
    • April 01: Talk by Manuel Galea, “Robust estimation in functional comparative calibration models via maximum Lq-likelihood” [Abstract].