Browsing by Author "Iglesias, Pilar"

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    A Bayesian Semiparametric Approach for Solving the Discrete Calibration Problem
    (TAYLOR & FRANCIS INC, 2010) Paz Casanova, Maria; Iglesias, Pilar; Bolfarine, Heleno
    In this article, we introduce a semi-parametric Bayesian approach based on Dirichlet process priors for the discrete calibration problem in binomial regression models. An interesting topic is the dosimetry problem related to the dose-response model. A hierarchical formulation is provided so that a Markov chain Monte Carlo approach is developed. The methodology is applied to simulated and real data.
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    Comparison between a measurement error model and a linear model without measurement error
    (ELSEVIER, 2008) Vidal, Ignacio; Iglesias, Pilar
    The regression of a response variable y on an explanatory variable from observations on (y, x), where x is a measurement of xi, is a special case of errors-in-variables model or measurement error model (MEM). In this work we attempt to answer the following question: given the data (y, x) under a MEM, is it possible to not consider the measurement error on the covariable in order to use a simpler model? To the best of our knowledge, this problem has not been treated in the Bayesian literature. To answer that question, we compute Bayes factors, the deviance information criterion and the posterior mean of the logarithmic discrepancy. We apply these Bayesian model comparison criteria to two real data sets obtaining interesting results. We conclude that, in order to simplify the MEM, model comparison criteria can be useful to compare structural MEM and a random effect model, but we would also need other statistic tools and take into account the final goal of the model. (c) 2008 Elsevier B.V. All rights reserved.
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    Explora: Un programa chileno de extensión en ciencia y tecnología en probabilidad y estadística
    (2001) Aravena Cuevas, Ricardo Hernán; Del Pino, Guido; Iglesias, Pilar
    La Comisión Chilena de Investigación en Ciencia y Tecnología (CONICYT) tiene programas de extensión coordinados por el denominado Programa Explora, el cual financia pequeños proyectos orientados principalmente a los niños. Este trabajo discute la experiencia de los autores con dos proyectos relacionados: Azar, Ciencia y Sociedad I y II, desarrollados en años consecutivos. Los proyectos estuvieron dirigidos principalmente a alumnos mayoritariamente con edades entre 15 y 17 años. En total hubo alrededor de 200 estudiantes, todos ellos seleccionados por sus profesores de Matemáticas, pertenecientes a 20 escuelas diferentes. Cada proyecto constó de tres módulos : Estadística y Medios de Comunicación, Análisis Exploratorio de Datos y Probabilidad. El primer módulo estaba dedicado a desarrollar el sentido común y el espíritu crítico para interpretar la información de los medios. El segundo formalizaba las ideas del primero, introduciendo los conceptos mediante la experimentación por los alumnos y con materiales con amplio uso de dibujos e historietas para vincular los conceptos a la vida cotidiana. Se enfatizaron las interpretaciones y se evitó el lenguaje matemático en la medida de lo posible. El último módulo trataba de la probabilidad, empleando un enfoque empírico, que involucraba tanto experimentos físicos como simulaciones.
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    Semiparametric Bayesian measurement error modeling
    (ELSEVIER INC, 2010) Casanova, Maria P.; Iglesias, Pilar; Bolfarine, Heleno; Salinas, Victor H.; Pena, Alexis
    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.