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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Search Results

Now showing 1 - 10 of 25

Epsilon contaminated priors in testing point null hypothesis: a procedure to determine the prior probability
(Statistics & Probability Letters, 2000) Gómez Villegas, Miguel Ángel; Sanz San Miguel, Luis
In this paper the problem of testing a point null hypothesis from the Bayesian perspective and the relation between this and the classical approach is studied. A procedure to determine the mixed prior distribution is introduced and a justification for this construction based on a measure of discrepancy is given. Then, we compare a lower bound for the posterior probability, when the prior is in the class of -contaminated distributions, of the point null hypothesis with the p-value.
Asymptotic relationships between posterior probabilities and p-values using the hazard rate
(Statistics & Probability Letters, 2004) Gómez Villegas, Miguel Ángel; Main Yaque, Paloma; Sanz San Miguel, Luis; Navarro Veguillas, Hilario
In this paper the asymptotic relationship between the classical p-value and the infimum (over all unimodal and symmetric distributions) of the posterior probability in the point null hypothesis testing problem is analyzed. It is shown that the ratio between the infimum and the classical p-value has an equivalent asymptotic behavior to the hazard rate of the sample model.
¿Por qué la inferencia estadística bayesiana?
(Boletín de estadística e investigación operativa : BEIO, 2006) Gómez Villegas, Miguel Ángel
En este artículo se pretende justifcar por qué se debe utilizar la aproximación bayesiana a la inferencia estadística. Como anunciaba Lindley en el primer Congreso Internacional de Estadística Bayesiana, falta menos para el 2021 año en el que el adjetivo bayesiana para la estadística sería superfluo al ser todas las aproximaciones a la estadística bayesianas.
Andrei Markov (1856-1922): en el 150 aniversario de su nacimiento
(BEIO, Boletín de Estadística e Investigación Operativa, 2006) Gómez Villegas, Miguel Ángel
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.
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.
A matrix variate generalization of the power exponential family of distributions
(Communications in statistics. Theory and methods, 2002) Gómez Sánchez-Manzano, Eusebio; Gómez Villegas, Miguel Ángel; Marín Diazaraque, Juan Miguel
This paper proposes a matrix variate generalization of the power exponential distribution family, which can be useful in generalizing statistical procedures in multivariate analysis and in designing robust alternatives to them. An example is added to show an application of the generalization.
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.