The impact of prior distributions on Bayesian variable selection methods

• Grant number: 24/00067-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2024
• End date: April 15, 2025
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Daiane Aparecida Zuanetti
• Grantee: João Vitor Giacomini
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

The process of identifying a subset of relevant variables in linear or non-linear models, called variable selection, has been a very recurrent topic of study in recent years, especially due to the vast amount of information and characteristics that the digital world provides. In this project, we will research, study and analyze the main Bayesian methods that have been used to select variables in linear models and the impact of the prior distributions used on the performance of these methods, discussing advantages and disadvantages of each methodology studied. Furthermore, we will list and analyze the algorithms that are already implemented and available for use, especially those based on MCMC. The implemented methods will initially be applied to synthetic data sets via simulation, mainly varying the value of the a priori variance of the regression coefficients, and finally to real data. Each methodology will be evaluated considering metrics called specificity and sensitivity, in addition to comparing the computational efficiency and time required to process each method.