Helio S. Migon

Dynamic Generalized Linear Models and Bayesian Forecasting

Abstract Dynamic Bayesian models are developed for application in nonlinear, non-normal time series and regression problems, providing dynamic extensions of standard generalized linear models. A key feature of the analysis is the use of conjugate prior and posterior distributions for the exponential family parameters. This leads to the calculation of closed, standard-form predictive distributions for forecasting and model criticism. The structure of the models depends on the time evolution of underlying state variables, and the feedback of observational information to these variables is achieved using linear Bayesian prediction methods. Data analytic aspects of the models concerning scale parameters and outliers are discussed, and some applications are provided. Dynamic Bayesian models are developed for application in nonlinear, non-normal time series and regression problems, providing dynamic extensions of standard generalized linear models. A key feature of the analysis is the use of conjugate prior and...

Dynamic Bayesian beta models

We develop a dynamic Bayesian beta model for modeling and forecasting single time series of rates or proportions. This work is related to a class of dynamic generalized linear models (DGLMs), although, for convenience, we use non-conjugate priors. The proposed methodology is based on approximate analysis relying on Bayesian linear estimation, nonlinear system of equations solution and Gaussian quadrature. Intentionally we avoid MCMC strategy, keeping the desired sequential nature of the Bayesian analysis. Applications to both real and simulated data are provided.

Bayesian approximations in randomized response model

Practical Bayesian inference depends upon detailed examination of posterior distribution. When the prior and likelihood are conjugate, this is easily carried out; however, in general, one must resort to numerical approximation. In this paper, our aim is to solve, using MAPLE, the Bayesian paradigm, for a very special data collecting procedure, known as the randomized-response technique. This allows researchers to obtain sensitive information while guaranteeing privacy to respondents. This approach intends to reduce false responses on sensitive questions. Exact methods and approximations will be compared from the accuracy point of view as well as for the computational effort.

Modelling zero-inflated spatio-temporal processes:

We consider models for spatio-temporal processes which assume either non-negative values, and often are observed as zero, or discrete values and are also inflated by zeros. Typically, in the first case, the spatial observations are obtained at fixed locations (point-referenced data) over a region D; whereas in the second, the region D is divided into a finite number of regular or irregular subregions (areal level), resulting in observations for each subregion. Our main idea is based on those of zeroinflated models, by assuming that the value observed at location s and time t, Yt (s), is a realization of a mixture between a Bernoulli distribution with a probability of success θt (s) and a probability density function or probability function p(yt (s) | .) For both cases, we include spatio-temporal latent processes in the model to account for the possible extra variation present in the mean structure of θt (s) and/or p(yt(s) | .). In the context of point-referenced data, we model the amount of rainfall over the city of Rio de Janeiro during 75 weeks; whereas in the areal data level case, we consider weekly cases of dengue fever in the city of Rio de Janeiro during the years of 2001–02.

Comovements and Contagion in Emergent Markets: Stock Indexes Volatilities

The past decade has witenessed a series of (well accepted and defined) financial crises periods in the world economy. Most of these events are country specific and eventually spreaded out across neighbor countries, with the concept of vicinity extrapolating the geographic maps and entering the contagion maps. Unfortunately, what contagion represents and how to measure it are still unanswered questions.

Bayesian spatial models for small area estimation of proportions

This article presents a logistic hierarchical model approach for small area prediction of proportions, taking into account both possible spatial and unstructured heterogeneity effects. The posterior distributions of the proportion predictors are obtained via Markov Chain Monte Carlo methods. This automatically takes into account the extra uncertainty associated with the hyperparameters. The procedures are applied to a real data set and comparisons are made under several settings, including a quite general logistic hierarchical model with spatial structure plus unstructured heterogeneity for small area effects. A model selection criterion based on the Expected Prediction Deviance is proposed. Its utility for selecting among competitive models in the small area prediction context is examined.

Bayesian binary regression model: an application to in-hospital death after AMI prediction

Um modelo bayesiano de regressao binaria e desenvolvido para predizer obito hospitalar em pacientes acometidos por infarto agudo do miocardio. Metodos de Monte Carlo via Cadeias de Markov (MCMC) sao usados para fazer inferencia e validacao. Uma estrategia para construcao de modelos, baseada no uso do fator de Bayes, e proposta e aspectos de validacao sao extensivamente discutidos neste artigo, incluindo a distribuicao a posteriori para o indice de concordância e analise de residuos. A determinacao de fatores de risco, baseados em variaveis disponiveis na chegada do paciente ao hospital, e muito importante para a tomada de decisao sobre o curso do tratamento. O modelo identificado se revela fortemente confiavel e acurado, com uma taxa de classificacao correta de 88% e um indice de concordância de 83%.

Bayesian outlier analysis in binary regression

We propose alternative approaches to analyze residuals in binary regression models based on random effect components. Our preferred model does not depend upon any tuning parameter, being completely automatic. Although the focus is mainly on accommodation of outliers, the proposed methodology is also able to detect them. Our approach consists of evaluating the posterior distribution of random effects included in the linear predictor. The evaluation of the posterior distributions of interest involves cumbersome integration, which is easily dealt with through stochastic simulation methods. We also discuss different specifications of prior distributions for the random effects. The potential of these strategies is compared in a real data set. The main finding is that the inclusion of extra variability accommodates the outliers, improving the adjustment of the model substantially, besides correctly indicating the possible outliers.

Forecasting the number of AIDS cases in Brazil

This paper presents a method to describe and forecast the incidence of AIDS in Brazil using time series models. The method is based on the class of generalized exponential growth models and uses the ideas of non- linear dynamic modelling. The aim is to provide good predictions and to inform sequentially on the asymptotic or explosive behaviour of the data series. Intervention to model unexpected changes in the data, on-line variance estimation and variance dependence on the mean are used to adequately model the data. The data are analyzed with some particular models from the above class and the: resulting inferences compared in terms of short-term and long-term predictive performance and model fit. Alternative approaches are considered and related data sets from Brazil and the UK are compared.

Stochastic volatility in mean models with heavy-tailed distributions

In this article, we introduce a likelihood-based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions (Abanto-Valle et al., 2012). Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. The method is based on the proposal of Langrock et al. (2012) and makes explicit the useful link between HMMs and SVM models with SMN distributions. Likelihood-based estimation of the parameters of stochastic volatility models in general, and SVM models with SMN distributions in particular, is usually regarded as challenging as the likelihood is a high-dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, i.e. estimating the volatility of the process.