Heteroscedastic controlled calibration model applied to analytical chemistry

In chemical analyses performed by laboratories, one faces the problem of determining the concentration of a chemical element in a sample. In practice, one deals with the problem using the so-called linear calibration model, which considers that the errors associated with the independent variables are negligible compared with the former variable. In this work, a new linear calibration model is proposed assuming that the independent variables are subject to heteroscedastic measurement errors. A simulation study is carried out in order to verify some properties of the estimators derived for the new model and it is also considered the usual calibration model to compare it with the new approach. Three applications are considered to verify the performance of the new approach. Copyright (C) 2010 John Wiley & Sons, Ltd.

On the skew-normal calibration model

In this article, we present the EM-algorithm for performing maximum likelihood estimation of an asymmetric linear calibration model with the assumption of skew-normally distributed error. A simulation study is conducted for evaluating the performance of the calibration estimator with interpolation and extrapolation situations. As one application in a real data set, we fitted the model studied in a dimensional measurement method used for calculating the testicular volume through a caliper and its calibration by using ultrasonography as the standard method. By applying this methodology, we do not need to transform the variables to have symmetrical errors. Another interesting aspect of the approach is that the developed transformation to make the information matrix nonsingular, when the skewness parameter is near zero, leaves the parameter of interest unchanged. Model fitting is implemented and the best choice between the usual calibration model and the model proposed in this article was evaluated by developing the Akaike information criterion, Schwarz`s Bayesian information criterion and Hannan-Quinn criterion.

Skew-normal linear calibration: a Bayesian perspective

In this paper, we present a Bayesian approach for estimation in the skew-normal calibration model, as well as the conditional posterior distributions which are useful for implementing the Gibbs sampler. Data transformation is thus avoided by using the methodology proposed. Model fitting is implemented by proposing the asymmetric deviance information criterion, ADIC, a modification of the ordinary DIC. We also report an application of the model studied by using a real data set, related to the relationship between the resistance and the elasticity of a sample of concrete beams. Copyright (C) 2008 John Wiley & Sons, Ltd.

A Log-Linear Regression Model for the Beta-Weibull Distribution

We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes, and censoring percentages, several simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.

Hypotheses testing for structural calibration model

The main objective of this paper is to discuss maximum likelihood inference for the comparative structural calibration model (Barnett, in Biometrics 25:129-142, 1969), which is frequently used in the problem of assessing the relative calibrations and relative accuracies of a set of p instruments, each designed to measure the same characteristic on a common group of n experimental units. We consider asymptotic tests to answer the outlined questions. The methodology is applied to a real data set and a small simulation study is presented.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

Aging and fluctuation-dissipation ratio in a nonequilibrium q-state lattice model

A generalized version of the nonequilibrium linear Glauber model with q states in d dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the q states. Exact expressions for the two-time autocorrelation and response functions on a d-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.

Contribution margin model applied to the marketing planning of a container liner carrier

The implementation of confidential contracts between a container liner carrier and its customers, because of the Ocean Shipping Reform Act (OSRA) 1998, demands a revision in the methodology applied in the carrier's planning of marketing and sales. The marketing and sales planning process should be more scientific and with a better use of operational research tools considering the selection of the customers under contracts, the duration of the contracts, the freight, and the container imbalances of these contracts are basic factors for the carrier's yield. This work aims to develop a decision support system based on a linear programming model to generate the business plan for a container liner carrier, maximizing the contribution margin of its freight.

Real time optimization (RTO) with model predictive control (MPC)

This paper studies a simplified methodology to integrate the real time optimization (RTO) of a continuous system into the model predictive controller in the one layer strategy. The gradient of the economic objective function is included in the cost function of the controller. Optimal conditions of the process at steady state are searched through the use of a rigorous non-linear process model, while the trajectory to be followed is predicted with the use of a linear dynamic model, obtained through a plant step test. The main advantage of the proposed strategy is that the resulting control/optimization problem can still be solved with a quadratic programming routine at each sampling step. Simulation results show that the approach proposed may be comparable to the strategy that solves the full economic optimization problem inside the MPC controller where the resulting control problem becomes a non-linear programming problem with a much higher computer load. (C) 2010 Elsevier Ltd. All rights reserved.

Time stability of soil water storage measured by neutron probe and the effects of calibration procedures in a small watershed

The knowledge of soil water storage (SWS) of soil profiles is crucial for the adoption of vegetation restoration practices. With the aim of identifying representative sites to obtain the mean SWS of a watershed, a time stability analysis of neutron probe evaluations of SWS was performed by the means of relative differences and Spearman rank correlation coefficients. At the same time, the effects of different neutron probe calibration procedures were explored on time stability analysis. mean SWS estimation. and preservation of the spatial variability of SWS. The selected watershed, with deep gullies and undulating slopes which cover an area of 20 ha, is characterized by an Ust-Sandiic Entisol and an Aeolian sandy soil. The dominant vegetation species are bunge needlegrass (Stipa bungeana Trim) and korshinsk peashrub (Carugano Korshinskii kom.). From June 11, 2007 to July 23,2008, SWS of the top1 m soil layer was evaluated for 20 dates, based on neutron probe data of 12 sampling sites. Three calibration procedures were employed: type 1, most complete, with each site having its own linear calibration equation (TrE); type II. with TrE equations extended over the whole field: and type III, with one single linear calibration curve for the whole field (UnE) and also correcting its intercept based on site specific relative difference analysis (RdE) and on linear fitting of data (RcE), both maintaining the same slope. A strong time stability of SWS estimated by TrE equations was identified. Soil particle size and soil organic matter content were recognized as the influencing factors for spatial variability of SWS. Land use influenced neither the spatial variability nor the time stability of SWS. Time stability analysis identified one site to represent the mean SWS of the whole watershed with mean absolute percentage errors of less than 10%, therefore. this site can be used as a predictor for the mean SWS of the watershed. Some equations of type II were found to be unsatisfactory to yield reliable mean SWS values or in preserving the associated soil spatial variability. Hence, it is recommended to be cautious in extending calibration equations to other sites since they might not consider the field variability. For the equations with corrected intercept (type III), which consider the spatial variability of calibration in a different way in relation to TrE, it was found that they can yield satisfactory means and standard deviation of SWS, except for the RdE equations, which largely leveled off the SWS values in the watershed. Correlation analysis showed that the neutron probe calibration was linked to soil bulk density and to organic matter content. Therefore, spatial variability of soil properties should be taken into account during the process of neutron probe calibration. This study provides useful information on the mean SWS observation with a time stable site and on distinct neutron probe calibration procedures, and it should be extended to soil water management studies with neutron probes, e.g., the process of vegetation restoration in wider area and soil types of the Loess Plateau in China. (C) 2009 Elsevier B.V. All rights reserved.

Classification model based on Raman spectra of selected morphological and biochemical tissue constituents for identification of atherosclerosis in human coronary arteries

This study presents the results of Raman spectroscopy applied to the classification of arterial tissue based on a simplified model using basal morphological and biochemical information extracted from the Raman spectra of arteries. The Raman spectrograph uses an 830-nm diode laser, imaging spectrograph, and a CCD camera. A total of 111 Raman spectra from arterial fragments were used to develop the model, and those spectra were compared to the spectra of collagen, fat cells, smooth muscle cells, calcification, and cholesterol in a linear fit model. Non-atherosclerotic (NA), fatty and fibrous-fatty atherosclerotic plaques (A) and calcified (C) arteries exhibited different spectral signatures related to different morphological structures presented in each tissue type. Discriminant analysis based on Mahalanobis distance was employed to classify the tissue type with respect to the relative intensity of each compound. This model was subsequently tested prospectively in a set of 55 spectra. The simplified diagnostic model showed that cholesterol, collagen, and adipocytes were the tissue constituents that gave the best classification capability and that those changes were correlated to histopathology. The simplified model, using spectra obtained from a few tissue morphological and biochemical constituents, showed feasibility by using a small amount of variables, easily extracted from gross samples.

Methods of Estimation in Multiple Linear Regression: Application to Clinical Data

Nesse artigo, tem-se o interesse em avaliar diferentes estratégias de estimação de parâmetros para um modelo de regressão linear múltipla. Para a estimação dos parâmetros do modelo foram utilizados dados de um ensaio clínico em que o interesse foi verificar se o ensaio mecânico da propriedade de força máxima (EM-FM) está associada com a massa femoral, com o diâmetro femoral e com o grupo experimental de ratas ovariectomizadas da raça Rattus norvegicus albinus, variedade Wistar. Para a estimação dos parâmetros do modelo serão comparadas três metodologias: a metodologia clássica, baseada no método dos mínimos quadrados; a metodologia Bayesiana, baseada no teorema de Bayes; e o método Bootstrap, baseado em processos de reamostragem.

On S-matrix factorization of the Landau-Lifshitz model

We consider the three-particle scattering S-matrix for the Landau-Lifshitz model by directly computing the set of the Feynman diagrams up to the second order. We show, following the analogous computations for the non-linear Schrdinger model [1, 2], that the three-particle S-matrix is factorizable in the first non-trivial order.

Improved score tests in symmetric linear regression models

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n(-3/2)), n being the sample size. The corrections represent an improvement over the corresponding original Rao`s score statistics, which are chi-squared distributed up to errors of order O(n(-1)). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

Local Influence Analysis for Skew-Normal Linear Mixed Models

In this article, we consider local influence analysis for the skew-normal linear mixed model (SN-LMM). As the observed data log-likelihood associated with the SN-LMM is intractable, Cook`s well-known approach cannot be applied to obtain measures of local influence. Instead, we develop local influence measures following the approach of Zhu and Lee (2001). This approach is based on the use of an EM-type algorithm and is measurement invariant under reparametrizations. Four specific perturbation schemes are discussed. Results obtained for a simulated data set and a real data set are reported, illustrating the usefulness of the proposed methodology.