Dealing with high complexity in spatio-temporal models

• Autores: Mario Figueira Pereira
• Directores de la Tesis: David Valentín Conesa Guillén (dir. tes.) , Antonio López Quílez (dir. tes.)
• Lectura: En la Universitat de València ( España ) en 2026
• Idioma: inglés
• Número de páginas: 406
• Tribunal Calificador de la Tesis: Jorge Mateu Mahiques (presid.) , Anabel Forte Deltell (secret.) , Sara Martino (voc.)
• Programa de doctorado: Programa Oficial de Doctorado en Estadística y Optimización
• Menciones:
  • Internacional
• Calificación: Sobresaliente Cum Laude
• Enlaces
  • Tesis en acceso abierto en:  TESEO  RODERIC 
• Resumen

  • In the current decade, significant advances have been achieved in both technological development and the design of new techniques for collecting data across a wide range of fields. Notable examples include the use of satellite imagery to assess forest cover through indices such as NDVI, EVI, and others; the systematic collection of traffic accident data; and the integration of multiple sources of information originating from oceanographic campaigns, autonomous vehicles that periodically collect data, and remote sensing technologies such as underwater gliders or aerial drones, for studying the distribution of marine species. These developments have not only given rise to new data structures but have also created scenarios marked by the availability of massive volumes of information—commonly referred to as Big Data.However, these diverse sources of information—due to their methods of acquisition or intrinsic characteristics—are often available at different spatial or temporal scales and exhibit varying levels of resolution. This can lead to inconsistencies and a lack of parsimony across datasets. Such a context demands a careful evaluation of the processes through which data are generated and collected, with special attention to sampling designs, data acquisition protocols, and the representational fidelity of each source.In response to these challenges, a wide array of new methodologies and approaches has been developed to appropriately handle the complexity and heterogeneity of modern data sources. Within the Bayesian paradigm, this methodological renewal has focused heavily on the development of spatial and spatio-temporal models, integrated frameworks that incorporate expert elicitation (from specialists on the field, institutions, or citizen science), and strategies designed to handle large-scale spatial datasets—either through dimensionality reduction or via sequential and distributed inference procedures.This thesis advances several key research directions related to the integration of heterogeneous data sources and the development of methods for handling complex data in Bayesian statistics, with a particular focus on methodological innovations within the Integrated Nested Laplace Approximations (INLA) framework. It tackles the integration of heterogeneous data sources by proposing coherent modeling strategies that account for differences in origin, scale, and reliability. The work introduces downscaling models within the context of Compositional Data Analysis to address spatially and spatio-temporally aggregated data, especially in cases where the aggregation support varies over time. It also explores sequential inference strategies that process information in subsets aligned with the model structure, enabling the combination of inferential results from the different data subsets. Finally, the thesis develops recursive and distributed inference methods that allow for real-time data analysis and are suitable for Big Data environments and scenarios where data privacy constraints preclude centralized processing.This thesis is primarily structured around a compendium of six research articles, complemented by introductory chapters, and a final chapter that presents developments from the later stages of the doctoral work, which are not yet available in article format. Chapter 1 introduces the statistical context—particularly within spatial domains—in a general and accessible manner.

    Chapter 2 outlines the inferential framework adopted throughout the thesis, providing a detailed exposition of the Integrated Nested Laplace Approximations (INLA) methodology. The core contributions, addressing the main research objectives, are presented in Chapters 3 through 8 and constitute the central body of the document. Chapter 9 presents the conclusions of the thesis along with several directions for future research.