Person:
Gómez Villegas, Miguel Ángel

First Name

Miguel Ángel

Last Name

Gómez Villegas

URI

https://hdl.handle.net/20.500.14352/75682

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Matemáticas

Department

Estadística e Investigación Operativa

Area

Estadística e Investigación Operativa

Identifiers

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Now showing 1 - 10 of 23

Comments to Objective Bayesian Point and Region Estimation in Location-Scale Models
(Sort: Statistics and Operations Research Transactions, 2007) Gómez Villegas, Miguel Ángel
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.
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, Luis
In 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.
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 Miguel
It 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.
epsilon-Contaminated priors in contingency tables
(Test, 2008) Gómez Villegas, Miguel Ángel; González Pérez, Beatriz
An 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.
Calculando la matriz de covarianzas con la estructura de una red Bayesiana Gaussiana
(2012) Gómez Villegas, Miguel Ángel; Susi García, María Del Rosario
En 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.
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 Ángel
El 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.
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, Luis
Recently, 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.
Bayesian analysis of contingency tables
(Communications in statistics. Theory and methods, 2005) Gómez Villegas, Miguel Ángel; González Pérez, Beatriz
The display of the data by means of contingency tables is used in different approaches to statistical inference, for example, to broach the test of homogeneity of independent multinomial distributions. We develop a Bayesian procedure to test simple null hypotheses versus bilateral alternatives in contingency tables. Given independent samples of two binomial distributions and taking a mixed prior distribution, we calculate the posterior probability that the proportion of successes in the first population is the same as in the second. This posterior probability is compared with the p-value of the classical method, obtaining a reconciliation between both results, classical and Bayesian. The obtained results are generalized for r × s tables.
Unimodal contaminations in testing point null hypothesis
(Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A: Matemáticas, 2003) Gómez Villegas, Miguel Ángel; Sanz San Miguel, Luis
The problem of testing a point null hypothesis from the Bayesian perspective is considered. The uncertainties are modelled through use of "{contamination class with the class of contaminations including: i) All unimodal distributions and ii). All unimodal and symmetric distributions. Over these classes, the in¯mum of the posterior probability of the point null hypothesis is computed and compared with the p{value and a better approach than the one known is obtained. [RESUMEN]Contaminaciones unimodales en el contraste de hip¶otesis nula puntual. Se considera el problema del contraste de hipótesis nula puntual desde el punto de vista Bayesiano. La incertidumbre se modeliza mediante el uso de la clase de las distribuciones "{contaminadas, cuando la clase de las contaminaciones incluye:i) todas las distribuciones unimodales y ii) todas las distribuciones unimodales y sim¶etricas. Se calcula el ínfimo de las probabilidades a posteriori de la hip¶otesis nula puntual sobre estas clases y se compara con el p{valor, obteniéndose una aproxi- mación aceptable entre ambos valores.