Bayesian Analysis for Nonlinear Regression Model Under Skewed Errors, with Application in Growth Curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew-t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.

Asymptotic Skewness in Exponential Family Nonlinear Models

In this article, we give an asymptotic formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in exponencial family nonlinear models. We generalize the result by Cordeiro and Cordeiro ( 2001). The formula is given in matrix notation and is very suitable for computer implementation and to obtain closed form expressions for a great variety of models. Some special cases and two applications are discussed.

Skovgaard`s adjustment to likelihood ratio tests in exponential family nonlinear models

Likelihood ratio tests can be substantially size distorted in small- and moderate-sized samples. In this paper, we apply Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-321] adjusted likelihood ratio statistic to exponential family nonlinear models. We show that the adjustment term has a simple compact form that can be easily implemented from standard statistical software. The adjusted statistic is approximately distributed as X(2) with high degree of accuracy. It is applicable in wide generality since it allows both the parameter of interest and the nuisance parameter to be vector-valued. Unlike the modified profile likelihood ratio statistic obtained from Cox and Reid [Cox, D.R., Reid, N., 1987. Parameter orthogonality and approximate conditional inference. journal of the Royal Statistical Society B49, 1-39], the adjusted statistic proposed here does not require an orthogonal parameterization. Numerical comparison of likelihood-based tests of varying dispersion favors the test we propose and a Bartlett-corrected version of the modified profile likelihood ratio test recently obtained by Cysneiros and Ferrari [Cysneiros, A.H.M.A., Ferrari, S.L.P., 2006. An improved likelihood ratio test for varying dispersion in exponential family nonlinear models. Statistics and Probability Letters 76 (3), 255-265]. (C) 2008 Elsevier B.V. All rights reserved.

Three-dimensional, fully adaptive simulations of phase-field fluid models

We present an efficient numerical methodology for the 31) computation of incompressible multi-phase flows described by conservative phase-field models We focus here on the case of density matched fluids with different viscosity (Model H) The numerical method employs adaptive mesh refinements (AMR) in concert with an efficient semi-implicit time discretization strategy and a linear, multi-level multigrid to relax high order stability constraints and to capture the flow`s disparate scales at optimal cost. Only five linear solvers are needed per time-step. Moreover, all the adaptive methodology is constructed from scratch to allow a systematic investigation of the key aspects of AMR in a conservative, phase-field setting. We validate the method and demonstrate its capabilities and efficacy with important examples of drop deformation, Kelvin-Helmholtz instability, and flow-induced drop coalescence (C) 2010 Elsevier Inc. All rights reserved

Stability of periodic optical solitons for a nonlinear Schrodinger system

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrodinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minima period. We also establish global well posedness for our system by using Bourgain`s approach.

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.

Influence diagnostics in Birnbaum-Saunders nonlinear regression models

We consider the issue of assessing influence of observations in the class of Birnbaum-Saunders nonlinear regression models, which is useful in lifetime data analysis. Our results generalize those in Galea et al. [8] which are confined to Birnbaum-Saunders linear regression models. Some influence methods, such as the local influence, total local influence of an individual and generalized leverage are discussed. Additionally, the normal curvatures for studying local influence are derived under some perturbation schemes. We also give an application to a real fatigue data set.

A note on influence diagnostics in nonlinear mixed-effects elliptical models

This paper provides general matrix formulas for computing the score function, the (expected and observed) Fisher information and the A matrices (required for the assessment of local influence) for a quite general model which includes the one proposed by Russo et al. (2009). Additionally, we also present an expression for the generalized leverage on fixed and random effects. The matrix formulation has notational advantages, since despite the complexity of the postulated model, all general formulas are compact, clear and have nice forms. (C) 2010 Elsevier B.V. All rights reserved.

Asymptotic skewness in Birnbaum-Saunders nonlinear regression models

The family of distributions proposed by Birnbaum and Saunders (1969) can be used to model lifetime data and it is widely applicable to model failure times of fatiguing materials. We give a simple matrix formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in Birnbaum-Saunders nonlinear regression models, recently introduced by Lemonte and Cordeiro (2009). The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors, in order to obtain closed-form skewness in a wide range of nonlinear regression models. Empirical and real applications are analyzed and discussed. (C) 2010 Elsevier B.V. All rights reserved.

Birnbaum-Saunders nonlinear regression models

We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear regression models potentially useful in lifetime data analysis. The class generalizes the regression model described by Rieck and Nedelman [Rieck, J.R., Nedelman, J.R., 1991. A log-linear model for the Birnbaum-Saunders distribution. Technometrics 33, 51-60]. We discuss maximum-likelihood estimation for the parameters of the model, and derive closed-form expressions for the second-order biases of these estimates. Our formulae are easily computed as ordinary linear regressions and are then used to define bias corrected maximum-likelihood estimates. Some simulation results show that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. Two empirical applications are analysed and discussed. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

Prigogine-Defay Ratio for an Ionic Glass-Former: Molecular Dynamics Simulations

The pressure dependence of the glass-transition temperature, T(g)(P), of the ionic glass-former 2Ca(NO(3))(2) center dot 3KNO(3), CKN, has been obtained by molecular dynamics (MD) simulations The liquid-glass difference of thermal expansivity, Delta alpha, heat capacity, Delta C(p), and isothermal compressibility, Delta kappa, have been calculated as a function of pressure. It has been found that the Ehrenfest relation dT(g)/dP = TV Delta alpha/Delta C(p) predicts the pressure dependence of T, but the other Ehrenfest relation, dT(g)/dP = Delta kappa/Delta alpha, does not. Consequently, the Prigogine-Defay ratio, Pi = Delta C(p)Delta kappa/TV Delta alpha(2), is Pi similar to 1.2 at low pressures, but increases 1 order of magnitude at high pressures. The pressure dependence of the Prigogine-Defay ratio is interpreted in light of recent explanations for the finding Pi > 1.

Alkoxy Chain Effect on the Viscosity of a Quaternary Ammonium Ionic Liquid: Molecular Dynamics Simulations

The viscosity of ionic liquids based on quaternary ammonium cations is reduced when one of the alkyl chains is replaced by an alkoxy chain (Zhou et al. Chem. Eur. J. 2005, 11, 752.). A microscopic picture of the role played by the ether function in decreasing the viscosity of quaternary ammonium ionic liquids is provided here by molecular dynamics (MD) simulations. A model for the ionic liquid N-ethyl-N,N-dimethyl-N-(2-methoxyethyl)ammonium bis(trifluoromethanesulfonyl)imide, MOENM(2)E TFSI, is compared to the tetraalky-lammonium counterpart. The alkoxy derivative has lower viscosity, higher ionic diffusion coefficients, and higher conductivity than the tetraalkyl system at the same density and temperature. A clear signature of the ether function on the liquid structure is observed in cation-cation correlations, but not in anion-anion or anion-cation correlations. In both the alkyl and the alkoxy ionic liquids, there is aggregation of long chains of neighboring cations within micelle-like structures. The MD simulations indicate that the less effective assembly between the more flexible alkoxy chains, in comparison to alkyl chains, is the structural reason for higher ionic mobility in MOENM(2)E TFSI.

Modelling water adsorption on Au(210) surfaces: II. Monte Carlo simulations

Canonical Monte Carlo simulations for the Au(210)/H(2)O interface, using a force field recently proposed by us, are reported. The results exhibit the main features normally observed in simulations of water molecules in contact with different noble metal surfaces. The calculations also assess the influence of the surface topography on the structural aspects of the adsorbed water and on the distribution of the water molecules in the direction normal to the metal surface plane. The adsorption process is preferential at sites in the first layer of the metal. The analysis of the density profiles and dipole moment distributions points to two predominant orientations. Most of the molecules are adsorbed with the molecular plane parallel to surface, while others adsorb with one of the O-H bonds parallel to the surface and the other bond pointing towards the bulk liquid phase. There is also evidence of hydrogen bond formation between the first and second solvent layers at the interface. (c) 2007 Elsevier B.V. All rights reserved.

Open Circuit Interaction of Formic Acid with Oxidized Pt Surfaces: Experiments, Modeling, and Simulations

We report in this work the study of the interaction between formic acid and an oxidized platinum surface under open circuit conditions. The investigation was carried out with the aid of in situ infrared spectroscopy, and results analyzed in terms of a mathematical model and numerical simulations. It has been found that during the first seconds of the interaction a small amount of CO(2) is produced and absolutely no adsorbed CO was observed. A sudden drop in potential then follows, which is accompanied by a steep increase first of CO(2) production and then by adsorbed CO. The steep transient was rationalized in terms of an autocatalytic production of free platinum sites which enhances the overall rate of reaction. Modeling and simulation showed nearly quantitative agreement with the experimental observations and provided further insight into some experimentally inaccessible variables such as surface free sites. Finally, based on the understanding provided from the combined experimental and theoretical approach, we discuss the general aspects influencing the open circuit transient.

Residual-based test for Nonlinear Cointegration with application in PPPs

Nested by linear cointegration first provided in Granger (1981), the definition of nonlinear cointegration is presented in this paper. Sequentially, a nonlinear cointegrated economic system is introduced. What we mainly study is testing no nonlinear cointegration against nonlinear cointegration by residual-based test, which is ready for detecting stochastic trend in nonlinear autoregression models. We construct cointegrating regression along with smooth transition components from smooth transition autoregression model. Some properties are analyzed and discussed during the estimation procedure for cointegrating regression, including description of transition variable. Autoregression of order one is considered as the model of estimated residuals for residual-based test, from which the teststatistic is obtained. Critical values and asymptotic distribution of the test statistic that we request for different cointegrating regressions with different sample sizes are derived based on Monte Carlo simulation. The proposed theoretical methods and models are illustrated by an empirical example, comparing the results with linear cointegration application in Hamilton (1994). It is concluded that there exists nonlinear cointegration in our system in the final results.