'New issues in matrix variate distributions: spatial and spatio-temporal data analysis'

• Grant number: 24/08369-8
• Support Opportunities: Scholarships abroad - Research
• Start date: January 15, 2025
• End date: January 14, 2026
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Carlos Alberto Ribeiro Diniz
• Grantee: Carlos Alberto Ribeiro Diniz
• Host Investigator: Victor Hugo Lachos Davila
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: University of Connecticut (UCONN), United States

Abstract

This research aims to develop and implement statistical modeling for clustering within a Bayesian framework in the context of multivariate spatial and spatiotemporal data. The statistical models for clustering will be used to identify patterns and structures in datasets that exhibit variations in both space and time. These models will take into account the geographic location of the observations as well as the temporal evolution of the variables over time. They will be designed to cluster observations that share similar characteristics in terms of spatial proximity and temporal patterns, thereby providing a more comprehensive understanding of the underlying processes.To achieve these objectives, we will employ mixtures of skewed matrix-variate distributions, such as the skewed matrix-t distribution and the generalized hyperbolic matrix distribution. Additionally, we will address the modeling of data in the presence of censoring and missing data, using both the EM algorithm and a Bayesian framework, leveraging the aforementioned skewed matrix-variate distributions. These studies are anticipated to make a substantial contribution to the advancement of understanding and applying statistical techniques that involve matrix-variate distributions in the analysis of complex three-dimensional data.