Functional data analysis: spatial association of curves and irregular spacing

• Autor(a) principal: Alvaro Alexander Burbano Moreno
• Data de Publicação: 2023
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/59365
• topic: B-spline; Bernstein polynomials; Bayesian inference; Gaussian Process; MCMC; Estatística – Teses; Análise Espacial (Estatística) – Teses; Inferência Bayesiana – Teses; Processos Gaussianos – Teses; Spline – Teses; Polinômios de Bernstein

Spatial Functional Data (SFD) analysis is an emerging statistical framework that combines Functional Data Analysis (FDA) and spatial dependency modeling. Unlike traditional statistical methods, which treat data as scalar values or vectors, SFD considers data as continuous functions, allowing for a more comprehensive understanding of their behavior and variability. This approach is well-suited for analyzing data collected over time, space, or any other continuous domain. SFD has found applications in various fields, including economics, finance, medicine, environmental science, and engineering. This thesis proposes new functional Gaussian models incorporating spatial dependence structures, focusing on irregularly spaced data and reflecting spatially correlated curves. The models are based on B-spline basis expansions and Bernstein Polynomials (BP) and utilize a Bayesian approach for estimating unknown quantities and parameters. The thesis explores the advantages and limitations of B-spline-based and BP-based models in capturing complex shapes and patterns while ensuring numerical stability. The main contributions of this work include the development of an innovative model designed for SFD using B-spline or BP structures, including a random effect to address associations between irregularly spaced observations, and a comprehensive simulation study to evaluate models' performance under various scenarios. The thesis also presents two real applications related to levels of PM10 and Temperature in Mexico City, showcasing practical illustrations of the proposed models.