Título: Multivariate linear regression models for asymmetric and heavy-tailed data
Data: 03/02/2021
Horario: 15:30h
Local: Transmissão online.
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Resumo: Multivariate linear regression models are formed by a vector of variables of interest/responses, a set of explanatory variables, a linear predictor formed by a linear combination of these explanatory variables and regression coefficients, and a random component that flexibilities the relationship systematic and the responses vector. Various experimental or observed phenomena in nature generate data with asymmetric behavior and/or heavy tails, such as phenotypic measurements in athletes, rainfall, among others. Thus, the usual hypothesis of normality of the data is relaxed using a more general class of distributions that incorporate asymmetry and heavy tails and have in particular cases the normal distribution, as well as other symmetrical/asymmetric distributions. In this lecture, we will approach some of these classes of distributions highlighting their properties, methods of parameter estimation, and applications in real data.
A sala será aberta sempre 10 minutos antes do início de cada sessão.
Título: Spatial Confounding Beyond Generalized Linear Mixed Models: Extension to Shared Components and Spatial Frailty Models
Palestrante: Marcos de Oliveira Prates (UFMG)
Data: 27/01/21
Horário: 15:30
Local: Transmissão online
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Resumo: Spatial confounding is defined as the confounding between the fixed and spatial random effects in generalized linear mixed models (GLMMs). It gained attention in the past years, as it may generate unexpected results in modeling. We introduce solutions to alleviate the spatial confounding beyond GLMMs for two families of statistical models. In the shared component models, multiple count responses are recorded at each spatial location, which may exhibit similar spatial patterns. Therefore, the spatial effect terms may be shared between the outcomes in addition to specifics spatial patterns. Our proposal relies on the use of modified spatial structures for each shared component and specific effects. Spatial frailty models can incorporate spatially structured effects and it is common to observe more than one sample unit per area which means that the support of fixed and spatial effects differs. Thus, we introduce a projection-based approach for reducing the dimension of the data. An R package named "RASCO: An R package to Alleviate Spatial Confounding" is provided. Cases of lung and bronchus cancer in the state of California are investigated under both methodologies and the results prove the efficiency of the proposed methodology.
Título: Bayesian Structured Additive Models: An application to car insurance data
Palestrante: Giovani L. Silva (Universidade de Lisboa)
Data: 16/12/2020
Horário: 15:30h
Local: Transmissão Online
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Resumo: This work was motivated by a car insurance study, comprising policies registered in Portugal mainland from 2011 to 2013, and involving some particularities, namely missing values and excess of zeros in the data set. It aims to analyse how claim frequency is influenced by policy risk factors in a car insurance application. Hence, risk profiles can be defined in order to apply adequate insurance premiums for policyholders and reduce monetary losses in insurance companies. The methodology is based on Structured Additive Models by using Bayesian approach via Markov chain Monte Carlo methods. Model selection suggested better fitting for zero-inflated negative binomial models, which were used for estimation of actuarial quantities of interest. Joint work with João Góis.
Título: The variational inference Lasso: selecting knots in a regression splines
Palestrante: Larissa de Carvalho Alves (ENCE)
Data: 13/01/2021
Horario: 15:30
Local: Transmissão online.
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Resumo: Recent literature finds many alternative proposals for modeling and estimating a smooth function. In this talk, I focus on the variants of smoothing splines, called penalized regression splines. This is an attractive approach to modeling the nonlinear smoothing effects of covariates. This study discusses the knots selection and a penalty is introduced to control the selection of knots. The approach will be through a full Bayesian Lasso with variational inference. Choosing the appropriate number of knots and their position is a difficult problem, therefore we propose a two steps procedure. 1. For a fixed number of knots we use a full Bayesian Lasso, which combines features of shrinkage and variable selection, to obtain the relevant knots; 2. The number of knots is chosen based on the evidence lower bound (ELBO) over a grid of values.
A sala será aberta sempre 10 minutos antes do início de cada sessão.
Título: Semi-parametric Bayesian models for heterogeneous degradation data: An application to Laser data
Palestrante: Rosangela H. Loschi (UFMG)
Data: 09/12/2020
Horario: 15:30
Local: Transmissão Online.
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Resumo: Degradation data are considered to make reliability assessments in highly reliable systems. The class of general path models is a popular tool to approach degradation data. In this class of models, the random effects correlate the degradation measures in each device. Random effects are interpreted in terms of the degradation rates, which facilitates the specification of their prior distribution. The usual approaches assume that the devices under test come from a homogeneous population. This assumption is strong, mainly, if the variability in the manufacturing process is high or there are no guarantees that the devices work on similar conditions. To account for heterogeneous degradation data, we develop semi-parametric degradation models based on the Dirichlet process mixture of both, normal and skew-normal distributions. The proposed model accommodates different shapes for the degradation rate distribution and also allows the estimation of the number of populations involved in the study. We prove that the proposed model also imposes heterogeneity in the lifetime data. We introduce a method to build the prior distributions which adapt previous approaches to the context in which mixture models fit latent variables. We carry out simulation studies and data analysis to show the flexibility of the proposed model in modeling skewness, heavy tail and multi-modal behavior of the random effects. Results show that the proposed models are competitive approaches to analyze degradation data. Joint work with Cristiano C. Santos.
A sala será aberta sempre 10 minutos antes do início de cada sessão.
