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Master's Dissertation
Full name
Ian Meneghel Danilevicz
Knowledge Area
Date of Defense
São Carlos, 2018
Ehlers, Ricardo Sandes (President)
Leandro, Roseli Aparecida
Prates, Marcos Oliveira
Title in English
Detecting Influential observations in spatial models using Bregman divergence
Keywords in English
Bayesian inference
Bregman divergence
Hamiltonian Monte Carlo
Influential points
spatial models
Abstract in English
How to evaluate if a spatial model is well ajusted to a problem? How to know if it is the best model between the class of conditional autoregressive (CAR) and simultaneous autoregressive (SAR) models, including homoscedasticity and heteroscedasticity cases? To answer these questions inside Bayesian framework, we propose new ways to apply Bregman divergence, as well as recent information criteria as widely applicable information criterion (WAIC) and leave-one-out cross-validation (LOO). The functional Bregman divergence is a generalized form of the well known Kullback-Leiber (KL) divergence. There is many special cases of it which might be used to identify influential points. All the posterior distributions displayed in this text were estimate by Hamiltonian Monte Carlo (HMC), a optimized version of Metropolis-Hasting algorithm. All ideas showed here were evaluate by both: simulation and real data.
Title in Portuguese
Detecção de observações influentes em modelos espaciais usando divergência de Bregman
Keywords in Portuguese
Divergência de Bregman
Inferência Bayesiana
Modelos espaciais
Monte Carlo Hamiltoniano
Pontos influentes
Abstract in Portuguese
Como avaliar se um modelo espacial está bem ajustado? Como escolher o melhor modelo entre muitos da classe autorregressivo condicional (CAR) e autorregressivo simultâneo (SAR), homoscedásticos e heteroscedásticos? Para responder essas perguntas dentro do paradigma bayesiano, propomos novas formas de aplicar a divergência de Bregman, assim como critérios de informação bastante recentes na literatura, são eles o widely applicable information criterion (WAIC) e validação cruzada leave-one-out (LOO). O funcional de Bregman é uma generalização da famosa divergência de Kullback-Leiber (KL). Há diversos casos particulares dela que podem ser usados para identificar pontos influentes. Todas as distribuições a posteriori apresentadas nesta dissertação foram estimadas usando Monte Carlo Hamiltoniano (HMC), uma versão otimizada do algoritmo Metropolis-Hastings. Todas as ideias apresentadas neste texto foram submetidas a simulações e aplicadas em dados reais.
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