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
9 results
Search Results
Now showing 1 - 9 of 9
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 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 epsilon-Contaminated priors in contingency tables(Test, 2008) Gómez Villegas, Miguel Ángel; González Pérez, BeatrizAn 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.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 Bayesian approach to model choice analysis in freight transport models (Case study: Central Bioceanic Railway Corridor)(Dyna, 2017) Gregorio Vicente, Óscar De; González Pérez, Beatriz; Gómez Villegas, Miguel ÁngelTransport planning requires tool to model the current and future situation of an infrastructures network. In this way, different scenarios of passenger flows, vehicles or freight can be predicted and serve as information for decision making. One of these tools are the so called "Demand models", among which the four steps models (Generation/attraction, Distribution, Modal choice, Network assignment) is a remarkable example for its widespread use. This paper presents a novel Bayesian approach to the third step of a demand transport model. Traditional discrete choice models are the ones most commonly used at this purpose, although other methods such as neural networks have been used by some authors. A Bayesian network is proposed as tool for estimating the decisions made by users when they face the need to choose which transport alternatives to use for sending cargo in a case study corresponding to the Central Bioceanic Corridor in South America. The results from fitting a logit model and a Bayesian network are compared and show the Bayesian network to be a promising tool to be applied in this kind of applications.Item The Multivariate Point Null Testing Problem: A Bayesian Discussion(Statistics & Probability Letters, 2008) Gómez Villegas, Miguel Ángel; González Pérez, BeatrizIn this paper the problem of testing a multivariate point hypothesis is considered. Of interest is the relationship between the p-value and the posterior probability. A Bayesian test for simple H0 V � D �0 versus bilateral H0 V 6D 0, with a mixed prior distribution for the parameter , is developed. The methodology consists of fixing a sphere of radius around 0 and assigning a prior mass,0, to H0 by integrating the density ./ over this sphere and spreading the remainder, 1 0, over H1 according to ./. A theorem that shows when the frequentist and Bayesian procedures can give rise to the same decision is proved. Then, some examples are revisited.Item A Bayesian Analysis For The Homogeneity Testing Problem Using Epsilon-Contaminated Priors(Communications in statistics. Theory and methods, 2011) Gómez Villegas, Miguel Ángel; González Pérez, BeatrizIn this article the problem of testing if r populations have the same distribution from a Bayesian perspective is studied using r × s contingency tables and ϵ–contaminated priors. A procedure to build a mixed prior distribution is introduced and a justification for this construction based on a measure of discrepancy is given. A lower bound for the posterior probabilities of the homogeneity null hypothesis, when the prior is in the class of ϵ–contaminated distributions, is calculated and compared numerically with the usual p-value. Examples show that the discrepancy between both is more acute when the mass assigned to the null in the mixed prior distribution is 0.5Item R X S Tables From A Bayesian Viewpoint(Revista matemática complutense, 2010) Gómez Villegas, Miguel Ángel; González Pérez, BeatrizThe display of the data by means of contingency tables is used for discussing different approaches to statistical inference. We develop a Bayesian procedure for the homogeneity testing problem of r populations using r × s contingency tables. The posterior probability of the homogeneity null hypothesis is calculated using a mixed prior distribution. The methodology consists of assigning an appropriate prior mass, π0, to the null and spreading the remainder, 1 − π0, over the alternative according to a density function. With this method, it is possible to prove a theorem which shows when the p-value and the posterior probability can give rise to the same conclusion.Item A condition to obtain the same decision in the homogeneity testing problem from the frequentist and Bayesian point of view(Communications in statistics. Theory and methods, 2006) Gómez Villegas, Miguel Ángel; González Pérez, BeatrizWe develop a Bayesian procedure for the homogeneity testing problem of r populations using r×s contingency tables. The posterior probability of the homogeneity null hypothesis is calculated using a mixed prior distribution. The methodology consist of choosing an appropriate value of π0 for the mass assigned to the null and spreading the remainder, 1 − π0, over the alternative according to a density function. With this method, a theorem which shows when the same conclusion is reached from both frequentist and bayesian points of view is obtained. A sufficient condition under which the p-value is less than a value α and the posterior probability is also less than 0.5 is provided.