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 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, LuisIn 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.Item 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, HilarioIn 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.Item ¿Por qué la inferencia estadística bayesiana?(Boletín de estadística e investigación operativa : BEIO, 2006) Gómez Villegas, Miguel ÁngelEn 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.Item Andrei Markov (1856-1922): en el 150 aniversario de su nacimiento(BEIO, Boletín de Estadística e Investigación Operativa, 2006) Gómez Villegas, Miguel ÁngelItem A Bayesian decision procedure for testing multiple hypotheses in DNA microarray experiments(Statistical Applications in Genetics and Molecular Biology, 2014) Gómez Villegas, Miguel Ángel; Salazar Mendoza, Isabel; Sanz San Miguel, LuisDNA microarray experiments require the use of multiple hypothesis testing procedures because thousands of hypotheses are simultaneously tested. We deal with this problem from a Bayesian decision theory perspective. We propose a decision criterion based on an estimation of the number of false null hypotheses (FNH), taking as an error measure the proportion of the posterior expected number of false positives with respect to the estimated number of true null hypotheses. The methodology is applied to a Gaussian model when testing bilateral hypotheses. The procedure is illustrated with both simulated and real data examples and the results are compared to those obtained by the Bayes rule when an additive loss function is considered for each joint action and the generalized loss 0-1 function for each individual action. Our procedure significantly reduced the percentage of false negatives whereas the percentage of false positives remains at an acceptable level.Item Bayesian analysis of contingency tables(Communications in statistics. Theory and methods, 2005) Gómez Villegas, Miguel Ángel; González Pérez, BeatrizThe 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.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 Evaluating The Difference Between Graph Structures In Gaussian Bayesian Networks(Expert Systems With Applications, 2011) Gómez Villegas, Miguel Ángel; Main Yaque, Paloma; Navarro Veguillas, Hilario; Susi García, María Del RosarioIn this work, we evaluate the sensitivity of Gaussian Bayesian networks to perturbations or uncertainties in the regression coefficients of the network arcs and the conditional distributions of the variables. The Kullback–Leibler divergence measure is used to compare the original network to its perturbation. By setting the regression coefficients to zero or non-zero values, the proposed method can remove or add arcs, making it possible to compare different network structures. The methodology is implemented with some case studies.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 Sensitivity to evidence in Gaussian Bayesian networks using mutual information(Information sciences, 2014) Gómez Villegas, Miguel Ángel; Main Yaque, Paloma; Viviani, PaolaWe introduce a methodology for sensitivity analysis of evidence variables in Gaussian Bayesian networks. Knowledge of the posterior probability distribution of the target variable in a Bayesian network, given a set of evidence, is desirable. However, this evidence is not always determined; in fact, additional information might be requested to improve the solution in terms of reducing uncertainty. In this study we develop a procedure, based on Shannon entropy and information theory measures, that allows us to prioritize information according to its utility in yielding a better result. Some examples illustrate the concepts and methods introduced.