Computational methods for approximated inference in Poisson spatial regression

• Grant number: 25/08612-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2025
• End date: May 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Aluísio de Souza Pinheiro
• Grantee: Gabriel Vieira Cardoso
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 23/02538-0 - Time Series, Wavelets, High Dimensional Data and Applications, AP.TEM

Abstract

Spatial covariance models have in general dense matrices. Therefore, estimation and prediction depend on approximations. This problem is a major concern in hierarchical models, such as the Poisson regression. We are going to study new approaches of approximate inference based upon Pólya-Gamma variables augmented likelihood via Hamiltonian Monte Carlo. We aim to provide concrete performance comparisons, both in terms of numerical efficiency as statistical losses due to the approximation method.