New perspectives for the Bayesian Conditional Transformation Models

• Ano de defesa: 2025
• Autor(a) principal: Piccirilli, Giovanni Pastori
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Aproximação de Laplace; B-splines; Bayes variacional; Bernstein polynomials; Conditional distribution function; Função de distribuição condicional; Laplace approximation; Polinômios de Bernstein; Variational Bayes
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45133/tde-19052025-140159/

Bayesian Conditional Transformation models (BCTMs) address the direct estimation of the conditional distribution function of a random variable conditional on a set of explanatory variables . These models infer the conditional distribution by applying a transformation function of given = , mapping it onto a baseline distribution free of parameters to be estimated. The benefit of these models is that the explanatory variables impact the entire conditional distribution of rather than only the first moments. The transformation functions are an essential part of the model and range from simple, low-parameterized functions to complex relationships involving nonlinear functions of the explanatory variables and re- sponse variables. In our approach, we explore the BCTM formulation that employs monotonic B-splines and Bernstein polynomials to parameterize the transformation function. Smoothness and regularization are ensured through appropriately chosen prior distributions for the parameters. We proposed two new estimation methods: one motivated by the Integrated Nested Laplace Approximation presented by Rue et al. (2009) and another using Variational Bayes presented by Niekerk and Rue (2024). Two simulation studies were conducted. One of them assesses the ability of our algorithm to recover the model coefficients, and the other evaluates its performance in estimating conditional densities compared to existing approaches. The applications were divided into two parts: (i) reanalysis of datasets previously studied using other methodologies and (ii) novel analyses of real-world data. In the first part, one of the studies compares our first proposed algorithm, named Integrated Laplace with Bayesian Conditional Transformation Models (ILBCTM), with the original MCMC-based algorithm for the BCTM (Carlan et al., 2023) on the same models. We obtained similar results with a smaller computational time. In the second part, we validate our methods through applications to real-world datasets, including a study on bronchial and lung cancer mortality in Brazil and an analysis of vehicle theft data in São Paulo city.