Agreement measures for spatio-temporal models with applications to image processing

The primary objective of the research is to develop new statistical methodologies and computational algorithms to assess the level of concordance (or agreement) between two spatiotemporal processes, including the comparison of two images or two georeferenced variables. Unlike traditional coefficients used in image processing—which omit coordinate information—this proposal seeks to generalize the concordance correlation coefficient and extend the probability of agreement by explicitly incorporating the georeferencing of the data.

Goals

The objetives are

• Define a model-free concordance correlation coefficient to measure the agreement between two spatial images.
• Propose a new concordance correlation coefficient for areal data by extending twofold multivariate Conditional Autoregressive (CAR) models to manage complex covariance structures.
• Develop the parametric framework for the proposed coefficients, including the study of probability of agreement estimation, score tests, and likelihood ratio tests.
• Evaluate and validate the performance of the developed methodologies through comprehensive Monte Carlo simulation studies and applications to real-world datasets, including Chilean poverty indices (CASEN), US soil contamination, and Harvard Forest data.

Principal Investigator

• Ronny Vallejos
  Universidad Técnica Federico Santa María

Collaborators

• Jonathan Acosta
  Pontificia Universidad Católica de Chile
• Aaron Ellison
  Harvard University
• Francisco Rodríguez
  Universidad Nacional de Colombia
• Clemente Ferrer
  Pontificia Universidad Católica de Chile
• Mario de Castro
  Universidade de São Paulo
• Felipe Osorio

Publications

• Vallejos, R. (2026). Agreement coefficients for continuous variables: A review. Environmetrics.
• Vallejos, R. , Acosta, J., Sepúlveda, B. (2026). Estimation of the rotation angle between two images by using the angular cross-variogram. Spatial Statistics 73, 100976.
• Vallejos,R., Ferrer, C., Mateu, J. (2025). A concordance coefficient for lattice data: An application to poverty indices in Chile. Spatial Statistics 70, 100936.
• Acosta, J., Vallejos, R ., García-Soidán, P. (2025). A penalized estimation of the variogram and effective sample size. Spatial Statistics 69, 100921.
• Ferrer, C., Vallejos, R. (2025). Is the effective sample size always less than n? A spatial regression approach. Statistics and Probability Letters 218, 110309.
• Acosta, J., Vallejos, R., Osorio, F., Ellison, A., de Castro, M. (2024). Comparing two spatial variables with the probability of agreement. Biometrics 80, ujae009.
• Gómez, J., Acosta, J., Vallejos, R., (2024). Correlation integral for stationary Gaussian time series. Sankhya A 86, 191-214.
• Pérez, J., Acosta, J., Vallejos, R., (2023). Assessing the estimation of nearly singular covariance matrices for modelling spatial variables. Electronic Journal of Statistics 17, 32873315.

Students

• Benjamin Bravo Thesis: Tamaño Muestral Efectivo para Modelos Lineales Generalizados.
  Ingeniería Civil Matemática y Magister en Ciencias Mención Matemática, UTFSM. (May 04, 2026).
• Sebastián Vidal Thesis: Impacto del preprocesamiento en la segmentación de imágenes.
  Ingeniería Civil Matemática, UTFSM. (December 27, 2024).
• Clemente Ferrer Thesis: A concordance coefficient for lattice data and effective sample size for spatial point processes.
  Ingeniería Civil Matemática y Magister en Ciencias Mención Matemática, UTFSM. (November 08, 2024).
• Eduardo Rubio Thesis: Propiedades estadísticas de la correlación integral.
  Ingeniería Civil Matemática, UTFSM. (October 28, 2024).
• Cloe Romero Thesis: Desempeño de la verosimilitud compuesta para datos espaciales de gran tamaño.
  Ingeniería Civil Matemática, UTFSM. (August 19, 2024).
• Pilar Cerda Thesis: Probabilidad de excedencia para problemas de contaminación espacial.
  Ingeniería Civil Matemática, UTFSM. (April 19, 2024).
• Fabián Castellano Thesis: Análisis de imágenes a través de la transformación de Box-Cox.
  Ingeniería Civil Matemática, UTFSM. (March 26, 2024).
• John Gómez Thesis: Correlation integral for spatial and temporal processes.
  Doctorado en Matemática, UTFSM. Co-advised by Jonathan Acosta. (December 05, 2023).
• Daniel Gajardo Thesis: Medidas generalizadas de correlación.
  Ingeniería Civil Matemática, UTFSM. (November 28, 2023).
• Javier Pizarro Thesis: Modelo predictivo basado en conceptos de machine learning enfocado en cobranza judicial.
  Ingeniería Civil Matemática, UTFSM. (October 31, 2023).
• Bastián Sepúlveda Thesis: Coeficiente de codispersión angular para detectar rotación de imágenes.
  Ingeniería Civil Matemática, UTFSM. (October 30, 2023).

Conference Presentations

2026

• Vallejos, R. “Statistical Agreement Measures for Image Data.” Geomed 2026, Pamplona, Spain. June 17-19, 2026.

2025

• Vallejos, R. “The Role of Image Preprocessing in Enhancing Segmentation Accuracy.” Spatial Statistics Conference, Noordwijk, The Netherlands. July 15-18, 2025.
• Vallejos, R. “Assessing the agreement between two continuous sequences.” METMA-LATAM II, Barranquilla, Colombia. June 25-27, 2025.
• Vallejos, R. “Statverse: A metaverse for teaching Statistics.” IV Congreso Colombiano de Estadística, Bogotá, Colombia. May 6-9, 2025.

2024

• Vallejos, R. “A novel coefficient for assessing agreement between two continuous variables.” SINAPE 2024, Fortaleza, Brazil. August 4-9, 2024.
• Vallejos, R. “A study of poverty in Chile through agreement coefficients for areal data.” METMA XI, Lancaster, UK. July 23-25, 2024.
• Vallejos, R. “Dos problemas desafiantes en el modelamiento de datos georeferenciados.” Invited Seminar, Facultad de Ingeniería en Minas y Energía, Universidad de Vigo, Spain. May 08, 2024.

2023

• Vallejos, R. “A coefficient to Measure Agreement Between Two Continuous Variables Based on a L1 Norm.” CMStatistics 2023, Berlin, Germany. December 15-17, 2023.
• Vallejos, R. “Assessing the Agreement Between two Spatial Variables.” Seminar, School of Mathematics, The University of Edinburgh, Scotland. October 20, 2023.
• Vallejos, R. “Coefficients of Concordance for Spatial Variables.” A New Era of Statistical Science, Belo Horizonte, Brazil. August 16-18, 2023.