Dynamic Weights in Gaussian Mixture Models: A Bayesian Approach

This paper proposes a generalization of Gaussian mixture models, where the mixture weight is allowed to behave as an unknown function of time. This model is capable of successfully capturing the features of the data, as demonstrated by simulated and real datasets. It can be useful in studies such as clustering, change-point and process control. In order to estimate the mixture weight function, we propose two new Bayesian nonlinear dynamic approaches for polynomial models, that can be extended to other problems involving polynomial nonlinear dynamic models. One of the methods, called here component-wise Metropolis-Hastings, apply the Metropolis-Hastings algorithm to each local level component of the state equation. It is more general and can be used in any situation where the observation and state equations are nonlinearly connected. The other method tends to be faster, but is applied specifically to binary data (using the probit link function). The performance of these methods of estimation, in the context of the proposed dynamic Gaussian mixture model, is evaluated through simulated datasets. Also, an application to an array Comparative Genomic Hybridization (aCGH) dataset from glioblastoma cancer illustrates our proposal, highlighting the ability of the method to detect chromosome aberrations

Wavelet-based estimators for mixture regression

We consider a process that is observed as a mixture of two random distributions, where the mixing probability is an unknown function of time. The setup is built upon a wavelet-based mixture regression. Two linear wavelet estimators are proposed. Furthermore, we consider three regularizing procedures for each of the two wavelet methods. We also discuss regularity conditions under which the consistency of the wavelet methods is attained and derive rates of convergence for the proposed estimators. A Monte Carlo simulation study is conducted to illustrate the performance of the estimators. Various scenarios for the mixing probability function are used in the simulations, in addition to a range of sample sizes and resolution levels. We apply the proposed methods to a data set consisting of array Comparative Genomic Hybridization from glioblastoma cancer studies461215234CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP308439/2014-72013/21273-5; 2013/09035-1; 2013/00506-1The authors thank an associate editor and two referees for the insightful suggestions and comments that led to a considerable improvement of this paper. The first author acknowledges FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) for the visit to the Georgia Institute of Technology (2013/21273‐5) and for his postdoc at the University of Campinas (2013/09035‐1). The second author acknowledges FAPESP (2013/00506‐1) and CNPq (308439/2014‐7). The third author acknowledges support from the National Center for Advancing Translational Sciences of the National Institutes of Health under Award UL1TR000454 and the Giglio Family Award from the Georgia Institute of Technolog