Marinho G. Andrade

Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics

The purpose of this paper is to develop a Bayesian analysis for nonlinear regression models under scale mixtures of skew-normal distributions. This novel class of models provides a useful generalization of the symmetrical nonlinear regression models since the error distributions cover both skewness and heavy-tailed distributions such as the skew-t, skew-slash and the skew-contaminated normal distributions. The main advantage of these class of distributions is that they have a nice hierarchical representation that allows the implementation of Markov chain Monte Carlo (MCMC) methods to simulate samples from the joint posterior distribution. In order to examine the robust aspects of this flexible class, against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. Further, some discussions on the model selection criteria are given. The newly developed procedures are illustrated considering two simulations study, and a real data previously analyzed under normal and skew-normal nonlinear regression models.

Zero-modified Poisson model: Bayesian approach, influence diagnostics, and an application to a Brazilian leptospirosis notification data

In this paper, a Bayesian method for inference is developed for the zero-modified Poisson (ZMP) regression model. This model is very flexible for analyzing count data without requiring any information about inflation or deflation of zeros in the sample. A general class of prior densities based on an information matrix is considered for the model parameters. A sensitivity study to detect influential cases that can change the results is performed based on the Kullback-Leibler divergence. Simulation studies are presented in order to illustrate the performance of the developed methodology. Two real datasets on leptospirosis notification in Bahia State (Brazil) are analyzed using the proposed methodology for the ZMP model.

Power series generalized nonlinear models

We introduce in this paper a new class of discrete generalized nonlinear models to extend the binomial, Poisson and negative binomial models to cope with count data. This class of models includes some important models such as log-nonlinear models, logit, probit and negative binomial nonlinear models, generalized Poisson and generalized negative binomial regression models, among other models, which enables the fitting of a wide range of models to count data. We derive an iterative process for fitting these models by maximum likelihood and discuss inference on the parameters. The usefulness of the new class of models is illustrated with an application to a real data set.

Seasonal streamflow forecasting via a neural fuzzy system

Abstract This paper presents a neural fuzzy system for seasonal streamflow forecasting. A rule base associated with linguistic terms such as “dry”, “medium”, and “wet” inflows was obtained through a statistical analysis of actual data and the results obtained with the model were compared with those of a multilayer feedforward artificial neural network and the Box & Jenkins model. The results for three Brazilian hydroelectric plants located in different river basins were compared on an one-step-abead basis. The results show a generally better performance of the neural fuzvy system for the cases studied

A numerical scheme based on mean value solutions for the Helmholtz equation on triangular grids

A numerical treatment for the Dirichlet boundary value problem on regular triangular grids for homogeneous Helmholtz equations is presented, which also applies to the convection-diffusion problems. The main characteristic of the method is that an accuracy estimate is provided in analytical form with a better evaluation than that obtained with the usual finite difference method. Besides, this classical method can be seen as a truncated series approximation to the proposed method. The method is developed from the analytical solutions for the Dirichlet problem on a ball together with an error evaluation of an integral on the corresponding circle, yielding O(h 4 ) accuracy. Some numerical examples are discussed and the results are compared with other methods, with a consistent advantage to the solution obtained here.

A Generalized Approach to the Modeling of the Species-Area Relationship

This paper proposes a statistical generalized species-area model (GSAM) to represent various patterns of species-area relationship (SAR), which is one of the fundamental patterns in ecology. The approach enables the generalization of many preliminary models, as power-curve model, which is commonly used to mathematically describe the SAR. The GSAM is applied to simulated data set of species diversity in areas of different sizes and a real-world data of insects of Hymenoptera order has been modeled. We show that the GSAM enables the identification of the best statistical model and estimates the number of species according to the area.

Transformed symmetric models

For the first time, we introduce a class of transformed symmetric models to extend the Box and Cox models to more general symmetric models. The new class of models includes all symmetric continuous distributions with a possible non-linear structure for the mean and enables the fitting of a wide range of models to several data types. The proposed methods offer more flexible alternatives to Box-Cox or other existing procedures. We derive a very simple iterative process for fitting these models by maximum likelihood, whereas a direct unconditional maximization would be more difficult. We give simple formulae to estimate the parameter that indexes the transformation of the response variable and the moments of the original dependent variable which generalize previous published results. We discuss inference on the model parameters. The usefulness of the new class of models is illustrated in one application to a real dataset.

Comparison between the complete Bayesian method and empirical Bayesian method for ARCH models using Brazilian financial time series

ABSTRACT. In this work we compared the estimates of the parameters of ARCH models using a com-plete Bayesian method and an empirical Bayesian method in which we adopted a non-informative priordistribution and informative prior distribution, respectively. We also considered a reparameterization ofthose models in order to map the space of the parameters into real space. This procedure permits choosingprior normal distributions for the transformed parameters. The posterior summaries were obtained usingMonte Carlo Markov chain methods (MCMC). The methodology was evaluated by considering the Telebrasseries from the Brazilian financial market. The results show that the two methods are able to adjust ARCHmodels with different numbers of parameters. The empirical Bayesian method provided a more parsimo-nious model to the data and better adjustment than the complete Bayesian method. Keywords : ARCH models, Bayesian approach, MCMC methods. 1 INTRODUCTION The dynamics of world financial markets requires increasingly sophisticated, complex and effi-cient models to describe the trends and characteristics of financial assets as accurately as possible.The analysis of financial series shows they have a high rate of change of the conditional variancein time. The square root of this rate (standard deviation) is called volatility. Understanding howvolatility changes over time is critical to the financial market, influencing the risk assessmentof investments and asset pricing. It determines the degree of change of the price of the asset inthe future,

Transformed GARMA model: Properties and simulations

ABSTRACT Real time series can present anomalies, like non-additivity, non-normality, and heteroscedasticity, which makes using GARMA models impossible. Our article introduces a new class of models called Transformed Generalized Autoregressive Moving Average (TGARMA) models that allow using transformations to guarantee the GARMA assumptions. We present an extensive simulation study of the influence of the transformation on GARMA estimation. We also propose using bootstrap methods to get more information about the distribution of the transformation parameter. We apply the methodology to data related to annual Swedish fertility rates.

ESTIMATIVA DA RELAÇÃO HIPSOMÉTRICA COM MODELOS NÃO LINEARES AJUSTADOS POR MÉTODOS BAYESIANOS EMPÍRICOS

Neste trabalho, esta sendo proposta uma abordagem bayesiana para resolver o problema de inferencia com restricoes nos parâmetros, em modelos nao lineares que representam a relacao hipsometrica em clones de Eucalyptus sp. As estimativas Bayesianas sao calculadas com a tecnica de simulacao de Monte Carlo em Cadeia de Markov (MCMC). O metodo proposto foi aplicado a diferentes conjuntos de dados reais, dos quais foram selecionados dois para mostrar os resultados obtidos. Estes foram comparados aos obtidos pelo metodo de minimos quadrados, destacando-se a superioridade da abordagem Bayesiana empirica proposta, uma vez que esta abordagem sempre gera resultados coerentes biologicamente para a relacao hipsometrica.