Bayesian estimation of dynamic mixture models by wavelets using Pólya-Gamma data augmentation

• Grant number: 26/14965-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2026
• End date: August 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Michel Helcias Montoril
• Grantee: Nicolas Magalhães Santana e Silva
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

Dynamic mixture models are powerful tools for identifying regime switches in bimodal data, with applications in hydrology, genomics, and other areas. Recently, Motta and Montoril (2026) proposed a Bayesian approach for estimating such models using wavelets, in which the dynamic mixture weights are modeled via a probit link, with inference based on the data augmentation scheme of Albert and Chib (1993). In this undergraduate research project, we propose to study and implement a natural alternative to this formulation: replacing the probit link with the logit link, with Bayesian inference enabled by the Pólya-Gamma data augmentation introduced by Polson et al. (2013). This data augmentation scheme yields closed-form full conditional distributions for all model parameters, preserving conjugacy and enabling the implementation of an efficient Gibbs sampler. The new formulation is expected to provide a competitive alternative to the probit approach, with exact mixture properties conferred by the Pólya-Gamma latent variable. Activities will be carried out over twelve months, including computational implementation in R, Monte Carlo simulation studies, and real-world data applications. (AU)