Bayesian estimation of regression parameters in elliptical measurement error models

The main object of this paper is to discuss the Bayes estimation of the regression coefficients in the elliptically distributed simple regression model with measurement errors. The posterior distribution for the line parameters is obtained in a closed form, considering the following: the ratio of the error variances is known, informative prior distribution for the error variance, and non-informative prior distributions for the regression coefficients and for the incidental parameters. We proved that the posterior distribution of the regression coefficients has at most two real modes. Situations with a single mode are more likely than those with two modes, especially in large samples. The precision of the modal estimators is studied by deriving the Hessian matrix, which although complicated can be computed numerically. The posterior mean is estimated by using the Gibbs sampling algorithm and approximations by normal distributions. The results are applied to a real data set and connections with results in the literature are reported. (C) 2011 Elsevier B.V. All rights reserved.

Semiparametric Bayesian measurement error modeling

This work presents a Bayesian semiparametric approach for dealing with regression models where the covariate is measured with error. Given that (1) the error normality assumption is very restrictive, and (2) assuming a specific elliptical distribution for errors (Student-t for example), may be somewhat presumptuous; there is need for more flexible methods, in terms of assuming only symmetry of errors (admitting unknown kurtosis). In this sense, the main advantage of this extended Bayesian approach is the possibility of considering generalizations of the elliptical family of models by using Dirichlet process priors in dependent and independent situations. Conditional posterior distributions are implemented, allowing the use of Markov Chain Monte Carlo (MCMC), to generate the posterior distributions. An interesting result shown is that the Dirichlet process prior is not updated in the case of the dependent elliptical model. Furthermore, an analysis of a real data set is reported to illustrate the usefulness of our approach, in dealing with outliers. Finally, semiparametric proposed models and parametric normal model are compared, graphically with the posterior distribution density of the coefficients. (C) 2009 Elsevier Inc. All rights reserved.

Multivariate measurement error models based on scale mixtures of the skew-normal distribution

Scale mixtures of the skew-normal (SMSN) distribution is a class of asymmetric thick-tailed distributions that includes the skew-normal (SN) distribution as a special case. The main advantage of these classes of distributions is that they are easy to simulate and have a nice hierarchical representation facilitating easy implementation of the expectation-maximization algorithm for the maximum-likelihood estimation. In this paper, we assume an SMSN distribution for the unobserved value of the covariates and a symmetric scale mixtures of the normal distribution for the error term of the model. This provides a robust alternative to parameter estimation in multivariate measurement error models. Specific distributions examined include univariate and multivariate versions of the SN, skew-t, skew-slash and skew-contaminated normal distributions. The results and methods are applied to a real data set.

Measurement error models with a general class of error distribution

In general, the normal distribution is assumed for the surrogate of the true covariates in the classical error model. This paper considers a class of distributions, which includes the normal one, for the variables subject to error. An estimation approach yielding consistent estimators is developed and simulation studies reported.

Influence Diagnostics for a Skew Extension of the Grubbs Measurement Error Model

Influence diagnostics methods are extended in this article to the Grubbs model when the unknown quantity x (latent variable) follows a skew-normal distribution. Diagnostic measures are derived from the case-deletion approach and the local influence approach under several perturbation schemes. The observed information matrix to the postulated model and Delta matrices to the corresponding perturbed models are derived. Results obtained for one real data set are reported, illustrating the usefulness of the proposed methodology.

A DISCRETIZATION SCHEME FOR AN ONE-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH DELAY AND ITS DYNAMICS

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution u, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

A robust Bayesian approach to null intercept measurement error model with application to dental data

Measurement error models often arise in epidemiological and clinical research. Usually, in this set up it is assumed that the latent variable has a normal distribution. However, the normality assumption may not be always correct. Skew-normal/independent distribution is a class of asymmetric thick-tailed distributions which includes the Skew-normal distribution as a special case. In this paper, we explore the use of skew-normal/independent distribution as a robust alternative to null intercept measurement error model under a Bayesian paradigm. We assume that the random errors and the unobserved value of the covariate (latent variable) follows jointly a skew-normal/independent distribution, providing an appealing robust alternative to the routine use of symmetric normal distribution in this type of model. Specific distributions examined include univariate and multivariate versions of the skew-normal distribution, the skew-t distributions, the skew-slash distributions and the skew contaminated normal distributions. The methods developed is illustrated using a real data set from a dental clinical trial. (C) 2008 Elsevier B.V. All rights reserved.

Flow injection analysis of ethyl xanthate by gas diffusion and UV detection as CS(2) for process monitoring of sulfide ore flotation

A sensitive and robust analytical method for spectrophotometric determination of ethyl xanthate, CH(3)CH(2)OCS(2)(-) at trace concentrations in pulp solutions from froth flotation process is proposed. The analytical method is based on the decomposition of ethyl xanthate. EtX(-), with 2.0 mol L(-1) HCl generating ethanol and carbon disulfide. CS(2). A gas diffusion cell assures that only the volatile compounds diffuse through a PTFE membrane towards an acceptor stream of deionized water, thus avoiding the interferences of non-volatile compounds and suspended particles. The CS(2) is selectively detected by UV absorbance at 206 nm (epsilon = 65,000 L mol(-1) cm(-1)). The measured absorbance is directly proportional to EtX(-) concentration present in the sample solutions. The Beer`s law is obeyed in a 1 x 10(-6) to 2 x 10(-4) mol L(-1) concentration range of ethyl xanthate in the pulp with an excellent correlation coefficient (r = 0.999) and a detection limit of 3.1 x 10(-7) mol L(-1), corresponding to 38 mu g L. At flow rates of 200 mu L min(-1) of the donor stream and 100 mu L min(-1) of the acceptor channel a sampling rate of 15 injections per hour could be achieved with RSD < 2.3% (n = 10, 300 mu L injections of 1 x 10(-5) mol L(-1) EtX(-)). Two practical applications demonstrate the versatility of the FIA method: (i) evaluation the free EtX(-) concentration during a laboratory study of the EtX(-) adsorption capacity on pulverized sulfide ore (pyrite) and (ii) monitoring of EtX(-) at different stages (from starting load to washing effluents) of a flotation pilot plant processing a Cu-Zn sulfide ore. (C) 2010 Elsevier By. All rights reserved.

Fast and reliable analyses of sulphite in fruit juices using a supramolecular amperometric detector encompassing in flow gas diffusion unit

A new compact system encompassing in flow gas diffusion unit and a wall-jet amperometric FIA detector, coated with a supramolecular porphyrin film, was specially designed as an alternative to the time-consuming Monier-Williams method, allowing fast, reproducible and accurate analyses of free sulphite species in fruit juices. In fact, a linear response between 0.64 and 6.4 ppm of sodium sulphite. LOD = 0.043 ppm, relative standard deviation of +/- 1.5% (n = 10) and analytical frequency of 85 analyses/h were obtained utilising optimised conditions. That superior analytical performance allows the precise evaluation of the amount of free sulphite present in foods, providing an important comparison between the standard addition and the standard injection methods. Although the first one is most frequently used, it was strongly influenced by matrix effects because of the unexpected reactivity of sulphite ions with the juice matrixes, leading to its partial consumption soon after addition. In contrast, the last method was not susceptible to matrix effects yielding accurate results, being more reliable for analytical purposes. (C) 2011 Elsevier Ltd. All rights reserved.

Modeling Information Diffusion in University Libraries: Assessing Peer Interaction Patterns as a Complex Dynamic System

This presentation was offered as part of the CUNY Library Assessment Conference, Reinventing Libraries: Reinventing Assessment, held at the City University of New York in June 2014.

Koldiffusionens inverkan på utmattnings-hållfastheten hos varmvalsade sexkantsstänger;The influence of carbon diffusion on the fatigue strength of hot rolled hexagonal rods

Helstångsborr och konstång kallas bergborrverktyg, som tillverkas av sexkantiga stänger med inre hål för ledning av spolvatten. Dessa spolhål är klädda med ferritiskt rostfritt stål. Innan valsning borras ett centrerat hål i stålämnet som ska valsas. I det borrade hålet appliceras ett rör av ferritiskt rostfritt stål och i det röret skjuts en manganstålskärna in. Efter valsning dras kärnan ut och ett spolhål med invändigt foder av rostfritt stål bildas. Under uppvärmningen och valsningen av stålämnet sker normalt en koldiffusion från manganstålskärnan till det rostfria fodret. Fodrets syfte är att skydda spolhålets yta mot erosion och korrosion.Syftet med arbetet var att hitta en metod som garanterar uppkolning av det invändiga fodret, samt att utreda vad uppkolningen betyder för den mekaniska hållfastheten i stängerna. Ett laboratorieförsök visade att det var bra, med avseende på uppkolning, att blanda stearat i kärnbestrykningsmedlet. Kärnbestrykningsmedlet penslas på manganstålskärnan innan den förs in i stålämnet som ska valsas, dess syfte är att minska friktionen vid kärnutdragningen efter valsning.Ett försök utfördes i valsverket med stearat i kärnbestrykningsmedlet. En grundlig undersökning utfördes på två hetor som valsats med stearat-bestrykningsmedel, samt på en traditionellt tillverkad heta för att ha som referens. Hetorna kapades till provstänger om 1,5 m, totalt undersöktes 55 st.Utvärderingen av verksförsöket visade att stängernas kvalitet blir tillräckligt bra om ingenting oförutsett händer i produktionen, oavsett om koltillskott är tillsatt i bestrykningsmedlet eller inte. Arbetet gav inte en garanterande metod, men visade att stängerna normalt håller hög kvalitet.