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
8 results
Search Results
Now showing 1 - 8 of 8
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 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 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, LuisThe 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.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.Item A Bayesian Analysis For The Multivariate Point Null Testing Problem(Statistics, 2009) Gómez Villegas, Miguel Ángel; Main Yaque, Paloma; Sanz San Miguel, LuisA Bayesian test for the point null testing problem in the multivariate case is developed. A procedure to get the mixed distribution using the prior density is suggested. For comparisons between the Bayesian and classical approaches, lower bounds on posterior probabilities of the null hypothesis, over some reasonable classes of prior distributions, are computed and compared with the p-value of the classical test. With our procedure, a better approximation is obtained because the p-value is in the range of the Bayesian measures of evidence.Item A Bayesian Test For The Mean Of The Power Exponential Distribution(Communications in statistics. Theory and methods, 2008) Gómez Villegas, Miguel Ángel; Portela García-Miguel, Javier; Sanz San Miguel, LuisIn this article, we deal with the problem of testing a point null hypothesis for the mean of a multivariate power exponential distribution. We study the conditions under which Bayesian and frequentist approaches can match. In this comparison it is observed that the tails of the model are the key to explain the reconciliability or irreconciliability between the two approaches.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.