Person: Gómez Villegas, Miguel Ángel
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First Name
Miguel Ángel
Last Name
Gómez Villegas
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Estadística e Investigación Operativa
Area
Estadística e Investigación Operativa
Identifiers
37 results
Search Results
Now showing 1 - 10 of 37
Item Comments to Objective Bayesian Point and Region Estimation in Location-Scale Models(Sort: Statistics and Operations Research Transactions, 2007) Gómez Villegas, Miguel ÁngelItem Response To Letter To The Editor(Communications in statistics. Theory and methods, 2001) Gómez, E.; Gómez Villegas, Miguel Ángel; Marin, J. M.This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions,claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.Item Assessing the effect of kurtosis deviations from Gaussianity on conditional distributions(Applied Mathematics and Computation, 2013) Gómez Villegas, Miguel Ángel; Main Yaque, Paloma; Navarro, H.; Susi García, María Del RosarioThe multivariate exponential power family is considered for n-dimensional random variables, Z, with a known partition Z equivalent to (Y, X) of dimensions p and n - p, respectively, with interest focusing on the conditional distribution Y vertical bar X. An infinitesimal variation of any parameter of the joint distribution produces perturbations in both the conditional and marginal distributions. The aim of the study was to determine the local effect of kurtosis deviations using the Kullback-Leibler divergence measure between probability distributions. The additive decomposition of this measure in terms of the conditional and marginal distributions, Y vertical bar X and X, is used to define a relative sensitivity measure of the conditional distribution family {Y vertical bar X = x}. Finally, simulated results suggest that for large dimensions, the measure is approximately equal to the ratio p/n, and then the effect of non-normality with respect to kurtosis depends only on the relative size of the variables considered in the partition of the random vector.Item A suitable Bayesian approach in testing point null hypothesis: some examples revisited(Communications in statistics. Theory and methods, 2002) Gómez Villegas, Miguel Ángel; Main Yaque, Paloma; Sanz San Miguel, LuisIn the problem of testing the point null hypothesis H-0: theta = theta(0) versus H-1: theta not equal theta(0), with a previously given prior density for the parameter theta, we propose the following methodology: to fix an interval of radius epsilon around theta(0) and assign a prior mass, pi(0), to H-0 computed by the density pi(theta) over the interval (theta(0) - epsilon, theta(0) + epsilon), spreading the remainder, 1 - pi(0), over H-1 according to pi(theta). It is shown that for Lindley's paradox, the Normal model with some different priors and Darwin-Fisher's example, this procedure makes the posterior probability of H-0 and the p-value matching better than if the prior mass assigned to H-0 is 0.5.Item Importance of the prior mass for agreement between frequentist and Bayesian approaches in the two-sided test(Statistics: A Journal of Theoretical and Applied Statistics, 2013) Gómez Villegas, Miguel Ángel; González Pérez, BeatrizA Bayesian test for H-0: = (0) versus H-1: (0) is developed. The methodology consists of fixing a sphere of radius around (0), assigning to H-0 a prior mass, (0), computed by integrating a density function () over this sphere, and spreading the remainder, 1(0), over H-1 according to (). The ultimate goal is to show when p values and posterior probabilities can give rise to the same decision in the following sense. For a fixed level of significance , when do (12) exist such that, regardless of the data, a Bayesian proponent who uses the proposed mixed prior with (0)((1), (2)) reaches, by comparing the posterior probability of H-0 with 1/2, the same conclusion as a frequentist who uses to quantify the p value? A theorem that provides the required constructions of (1) and (2) under verification of a sufficient condition ((12)) is proved. Some examples are revisited.Item Multivariate exponential power distributions as mixtures of normal distributions with Bayesian applications(Communications in statistics. Theory and methods, 2008) Gómez Sánchez-Manzano, Eusebio; Gómez Villegas, Miguel Ángel; Marín Diazaraque, Juan MiguelIt is shown that a multivariate exponential power distribution is a scale mixture of normal distributions, with respect to a probability distribution function, when its kurtosis parameter belongs to the interval (0,1]. The corresponding mixing probability distribution function is presented. This result is used to design a Bayesian hierarchical model and an algorithm to generate samples of the posterior distribution; these are applied to a problem of Quantitative Genetics.Item epsilon-Contaminated priors in contingency tables(Test, 2008) Gómez Villegas, Miguel Ángel; González Pérez, BeatrizAn r x s table is used for different approaches to statistical inference. We develop a Bayesian procedure to test simple null hypotheses versus bilateral alternatives in contingency tables. We consider testing equality of proportions of independent multinomial distributions when the common proportions are known. A lower bound of the posterior probabilities of the null hypothesis is calculated with respect to a mixture of a point prior on the null and an epsilon-contaminated prior on the proportions under the alternative. The resulting Bayes tests are compared numerically to Pearson's chi(2) in a number of examples. For the examined examples the lower bound and the p-value can be made close. The obtained results are generalized when the common proportions vector under the null is unknown or has a known functional form.Item Calculando la matriz de covarianzas con la estructura de una red Bayesiana Gaussiana(2012) Gómez Villegas, Miguel Ángel; Susi García, María Del RosarioEn este trabajo se introduce una fórmula recursiva que permite calcular la matriz de covarianzas de una red Bayesiana Gaussiana dados los parámetros de la especificación condicionada de la parte cuantitativa del modelo. Además se determinan las varianzas y las covarianzas del problema considerando los distintos caminos que aparecen en el grafo que recoge la parte cualitativa de la red.Item El «Ensayo encaminado a resolver un problema en la doctrina del azar»(Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A: Matemáticas, 2001) Gómez Villegas, Miguel ÁngelEl trabajo consta de una introducción biográfica en el que se recogen las pocas cosas que se conocen de la vida de Thomas Bayes. A continuación se tratan los antecedentes del problema de la probabilidad inversa y se comenta el Ensayo. Se recogen también tres aplicaciones añadidas al trabajo original de Thomas Bayes por Richard Price. Se incluyen las opiniones que el Ensayo ha suscitado a algunos eminentes estadísticos. [ABSTRACT] This work starts with a biographical introduction inc1uding a few things known of Thomas Bayes life. It is followed by the background to the inverse probability problem and the comments about the Essay. Three applications added to the original job of Thomas Bayes by Richard Price are included. Several opinions about the Essay given by some scientific figures are embodied at the end of the paper.Item Bayesian Analysis of Multiple Hypothesis Testing with Applications to Microarray Experiments(Communications in statistics. Theory and methods, 2011) Ausin, A. C.; Gómez Villegas, Miguel Ángel; González Pérez, Beatriz; Rodríguez Bernal, María Teresa; Salazar Mendoza, Isabel; Sanz San Miguel, LuisRecently, the field of multiple hypothesis testing has experienced a great expansion, basically because of the new methods developed in the field of genomics. These new methods allow scientists to simultaneously process thousands of hypothesis tests. The frequentist approach to this problem is made by using different testing error measures that allow to control the Type I error rate at a certain desired level. Alternatively, in this article, a Bayesian hierarchical model based on mixture distributions and an empirical Bayes approach are proposed in order to produce a list of rejected hypotheses that will be declared significant and interesting for a more detailed posterior analysis. In particular, we develop a straightforward implementation of a Gibbs sampling scheme where all the conditional posterior distributions are explicit. The results are compared with the frequentist False Discovery Rate (FDR) methodology. Simulation examples show that our model improves the FDR procedure in the sense that it diminishes the percentage of false negatives keeping an acceptable percentage of false positives.