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
7 results
Search Results
Now showing 1 - 7 of 7
Item 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 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 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.Item The effect of block parameter perturbations in Gaussian Bayesian networks: Sensitivity and robustness(Information Sciences, 2013) Gómez Villegas, Miguel Ángel; Main Yaque, Paloma; Susi García, María Del Rosarion this work we study the effects of model inaccuracies on the description of a Gaussian Bayesian network with a set of variables of interest and a set of evidential variables. Using the Kullback-Leibler divergence measure, we compare the output of two different networks after evidence propagation: the original network, and a network with perturbations representing uncertainties in the quantitative parameters. We describe two methods for analyzing the sensitivity and robustness of a Gaussian Bayesian network on this basis. In the sensitivity analysis, different expressions are obtained depending on which set of parameters is considered inaccurate. This fact makes it possible to determine the set of parameters that most strongly disturbs the network output. If all of the divergences are small, we can conclude that the network output is insensitive to the proposed perturbations. The robustness analysis is similar, but considers all potential uncertainties jointly. It thus yields only one divergence, which can be used to confirm the overall sensitivity of the network. Some practical examples of this method are provided, including a complex, real-world problemItem Sensitivity to hyperprior parameters in Gaussian Bayesian networks(Journal of multivariate analysis, 2014) Gómez Villegas, Miguel Ángel; Main Yaque, Paloma; Navarro, H.; Susi García, María Del RosarioBayesian networks (BNs) have become an essential tool for reasoning under uncertainty in complex models. In particular, the subclass of Gaussian Bayesian networks (GBNs) can be used to model continuous variables with Gaussian distributions. Here we focus on the task of learning GBNs from data. Factorization of the multivariate Gaussian joint density according to a directed acyclic graph (DAG) provides an alternative and interchangeable representation of a GBN by using the Gaussian conditional univariate densities of each variable given its parents in the DAG. With this latter conditional specification of a GBN, the learning process involves determination of the mean vector, regression coefficients and conditional variances parameters. Some approaches have been proposed to learn these parameters from a Bayesian perspective using different priors, and therefore some hyperparameter values are tuned. Our goal is to deal with the usual prior distributions given by the normal/inverse gamma form and to evaluate the effect of prior hyperparameter choice on the posterior distribution. As usual in Bayesian robustness, a large class of priors expressed by many hyperparameter values should lead to a small collection of posteriors. From this perspective and using Kullback-Leibler divergence to measure prior and posterior deviations, a local sensitivity measure is proposed to make comparisons. If a robust Bayesian analysis is developed by studying the sensitivity of Bayesian answers to uncertain inputs, this method will also be useful for selecting robust hyperparameter values.Item The dynamic linear model: an application to flood forecasting(Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales., 1999) Gómez Sánchez-Manzano, Eusebio; Gómez Villegas, Miguel Ángel; Tejada Cazorla, Juan AntonioThis paper introduces the Bayesian Dynamic Linear Model to predict the flows (mainly in flood conditions) at a point of a river in successive instants of time, knowing the previous flows at several stations located up the river. The model is fitted to a Spanish river rises.