Browsing by Author "Iglesias, P"

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    Bayesian analysis of the calibration problem under elliptical distributions
    (ELSEVIER SCIENCE BV, 2000) Branco, M; Bolfarine, H; Iglesias, P; Arellano Valle, RB
    In this paper we discuss calibration problems under dependent and independent elliptical family of distributions. In the dependent case, it is shown that the posterior distribution of the quantity of interest is robust with respect to the distributions in the elliptical family. In particular, the results obtained by Hoadley (1970. J. Amer. Statist. 65, 356-369) showing that the inverse estimator is a Bayes estimator under normal models with a Student-t prior also holds under the dependent elliptical family of distributions. In the independent case, the use of the elliptical family allows the consideration of models which provide protection against possible outliers in the data. The multivariate calibration problem is also considered, where some results given in Brown (1993. Measurement, Regression and Calibration. Oxford University Press, Oxford) are extended. Finally, the results of the paper are applied to a real data problem, showing that the Student-t model can be a valid alternative to normality. (C) 2000 Elsevier Science B.V. All rights reserved.
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    Bayesian calibration under a student-t model
    (SPRINGER HEIDELBERG, 1998) Branco, M; Bolfarine, H; Iglesias, P
    In this paper we consider linear calibration problems in regressions models with independent errors distributed according to the Student-t distribution. The approach followed is Bayesian, thus, involving the need for the specification of prior distributions for the model parameters. It is shown that the problem is equivalent to considering an heteroscedastic regression model with an appropriate prior distributions on the model variances. By considering this alternative construction for the Student-t calibration model it is possible to use the Gibbs sampler to estimate the marginal posterior distributions. Simulation studies are reported which illustrate the performance of the approach proposed. An application to a data set analyzed by Smith and Corbett (1987) on measuring marathon courses is considered by using the approach developed in the paper.
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    Bayesian inference in spherical linear models: robustness and conjugate analysis
    (ELSEVIER INC, 2006) Arellano Valle, RB; del Pino, G; Iglesias, P
    The early work of Zellner on the multivariate Student-t linear model has been extended to Bayesian inference for linear models with dependent non-normal error terms, particularly through various papers by Osiewalski, Steel and coworkers. This article provides a full Bayesian analysis for a spherical linear model. The density generator of the spherical distribution is here allowed to depend both on the precision parameter phi and on the regression coefficients beta. Another distinctive aspect of this paper is that proper priors for the precision parameter are discussed.
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    Data analysis using regression models with missing observations and long-memory: an application study
    (ELSEVIER, 2006) Iglesias, P; Jorquera, H; Palma, W
    The objective of this work is to propose a statistical methodology to handle regression data exhibiting long memory errors and missing values. This type of data appears very often in many areas, including hydrology and environmental sciences, among others. A generalized linear model is proposed to deal with this problem and an estimation strategy is developed that combines both classical and Bayesian approaches. The estimation methodology proposed is illustrated with an application to air pollution data which shows the impact of the long memory in the statistical inference and of the missing values on the computations. From a Bayesian standpoint, genuine priors are considered for the parameters of the model which are justified within the context of the air pollution model derivation. (c) 2005 Elsevier B.V. All rights reserved.