A Bayesian approach for left-censored data based on mixture and semi-continuous models using Tobit structure

• Autor(a) principal: Peralta, Danielle
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/17/17139/tde-10042023-155349/
• topic: Análise Bayesiana; Análise de dados; Dados com censuras à esquerda; Distribuição de Weibull; Métodos MCMC; Modelo de Tobit

The main objective of this thesis is to introduce a left-censored data analysis using the tobit model for univariate and multivariate data. The tobit model can be used as an alternative to the least squares regression model when the assumption of linearity is not satisfied. The tobit model is able to fit the data adequately by formulating a regression model for which the response is pre-fixed to a limit value. In this thesis we present five chapters, each considering a manuscript submitted for publication and with different approaches and applications. The estimation of the model parameters is performed using Bayesian inference methods. The summaries a posteriori of interest are obtained using existing MCMC (Monte Carlo on Markov Chains) simulation methods, as Gibs and Metropolis-Hasting. In the first paper (Chapter 2) we present the tobit-Weibull mixture model to analyze environmental data under the left censoring scheme. The considered dataset is related to ammonia nitrogen concentrations in rivers. In the second paper (Chapter 3), the bivariate tobit-Weibull model under a hierarchical Bayesian analysis is presented considering a dataset in stellar astronomy where a fragility or latent variable is considered to capture the possible correlation between the bivariate responses for the same sample unit; applications of the univariate and bivariate tobit-Weibull model are also presented in Chapter 4, considering two medical datasets (cancer survival data and vaccine data). The tobit-Weibull model in the presence of some covariates with linear and quadratic effects, under the left censoring scheme, is presented in Chapter 5 considering a dataset concerning total daily precipitation collected at a weather station located in the city of São Paulo, Brazil. In Chapter 6 we present a generalized form of the tobit-Weibull model in the presence of covariates and excess zeros; the application was performed using data concerning total daily precipitation. Chapter 7 concludes this thesis with general conclusions showing the usefulness of the proposed model fot analyzing left-censored data or with an excess of zero-valued observations.