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Master's Dissertation
Full name
Flávia Castro Motta
Knowledge Area
Date of Defense
São Carlos, 2023
Montoril, Michel Helcias (President)
Chiann, Chang
Nobre, Widemberg da Silva
Title in English
Bayesian estimation of dynamic mixture models by wavelets
Keywords in English
Change-point detection
Mixture problem
Spike and slab prior
Wavelet empirical Bayes
Abstract in English
Gaussian mixture models are used successfully in various statistical learning applications. The good results provided by these models encourage several generalizations of them. Among possible adaptations, one can assume a dynamic behavior for the mixture weights to make the model more adaptive to different data sets. When estimating this dynamic behavior, wavelet bases have emerged as an alternative. However, in the existing literature, the wavelet-based methods only estimate the dynamic mixing probabilities, failing to provide estimates for the component parameters of the mixture model. In this work, we propose two approaches based on orthonormal wavelets to estimate the dynamic mixture weights under efficient MCMC algorithms that allows us to estimate the component parameters from their posterior samples. We use simulated and real data sets to illustrate both approaches performances. The results indicate that the proposed methods are promising and computationally efficient alternatives for estimating jointly the dynamic weights and the component parameter of two Gaussian mixtures.
Title in Portuguese
Estimação Bayesiana de modelos de mistura dinâmica por ondaletas
Keywords in Portuguese
Bayes empírico em ondaletas
Detecção de ponto de mudança
Priori spike e slab
Problema de mistura
Abstract in Portuguese
Modelos de mistura gaussiana são usados com sucesso em várias aplicações de aprendizado estatístico. Os bons resultados fornecidos por esses modelos incentivam diversas generalizações destes. Entre as possíveis adaptações, pode-se supor um comportamento dinâmico para os pesos da mistura para tornar o modelo mais adaptável a diferentes conjuntos de dados. Ao estimar esse comportamento dinâmico, bases de ondaletas surgem como uma alternativa. No entanto, na literatura existente, os métodos baseados em ondaletas apenas estimam os pesos dinâmicos da mistura, não fornecendo estimativas para os parâmetros das componentes do modelo. Neste trabalho, propomos duas abordagens baseadas em ondaletas ortonormais para estimar o comportamento dinâmico do peso da mistura sob algoritmos MCMC eficientes que nos permitem estimar os parâmetros das componentes a partir de suas amostras posteriores. Usamos conjuntos de dados simulados e reais para ilustrar o desempenho de ambas as abordagens. Os resultados indicam que os métodos propostos são alternativas promissoras e computacionalmente eficientes para estimar misturas gaussianas dinâmicas.
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