Person: González Pérez, Beatriz
Universidad Complutense de Madrid
Faculty / Institute
Estadística e Investigación Operativa
Estadística e Investigación Operativa
Now showing 1 - 10 of 10
- PublicationA condition to obtain the same decision in the homogeneity testing problem from the frequentist and Bayesian point of view(Marcel Dekker, 2006-12-12) Gómez Villegas, Miguel A.; 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.
- PublicationImportance of the prior mass for agreement between frequentist and Bayesian approaches in the two-sided test(Taylor & Francis Group Ltd, 2013-06) Gómez Villegas, Miguel A.; 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.
- PublicationBayesian approach to model choice analysis in freight transport models (Case study: Central Bioceanic Railway Corridor)(Asociación Nacional de Ingenieros Industriales de España, 2017) De Gregorio Vicente, Oscar; González Pérez, Beatriz; Gómez Villegas, Miguel A.Transport 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.
- PublicationThe Multivariate Point Null Testing Problem: A Bayesian Discussion(Elsevier Science, 2008) Gómez Villegas, Miguel A.; 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.
- PublicationA Bayesian Analysis For The Homogeneity Testing Problem Using Epsilon-Contaminated Priors(Taylor & Francis, 2011) Gómez Villegas, Miguel A.; 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 0.5
- PublicationR X S Tables From A Bayesian Viewpoint(Universidad Complutense de Madrid, 2010) Gómez Villegas, Miguel A.; 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.
- PublicationBayesian Analysis of Multiple Hypothesis Testing with Applications to Microarray Experiments(Taylor & Francis, 2011) Gómez Villegas, Miguel A.; Ausin, A.C; González Pérez, Beatriz; Rodríguez-Bernal, María Teresa; Salazar, I.; 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.
- PublicationBayesian analysis of contingency tables(Marcel Dekker Inc, 2005-08-08) Gómez Villegas, Miguel A.; 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.
- Publicationepsilon-Contaminated priors in contingency tables(Springer, 2008-05) Gómez Villegas, Miguel A.; 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.
- PublicationAn Explanatory Analysis of Electricity Prices within Day-Ahead Spanish Energy Market by Using a Graphical Automatization with R(IEEE, 2014) Velasco, J.M.; González Pérez, Beatriz; Minana, Guadalupe; López, Victoria; Caro, RaquelSince 1998, the Spanish and Portuguese Administrations began to share a common path in building the Iberian Electricity Market (MIBEL). This cooperation has been very successful, not only for its contribution to the existence of an electricity market on an Iberian level, but also on a European scale, as a significant step in building the Internal Energy Market. The price of electricity in the MIBEL is very changeable. This creates a lot of uncertainty and risk in market actors. Due to continuous changes in demand and marginal price adjustment, buyers and sellers can not know in advance the evolution of prices. Our interest is to study of this uncertainty since the perspective of the buyer and not the seller's perspective. The aim of this work is to develop a graphical analysis of the variables involved in the Spanish Energy Market in order to explain the electric price and provide to small traders, that could be interested in participating in that market, better knowledge of the schedule. On the other hand, large industrial consumers use this information to design strategies to optimize its production capacity and improve their production costs. In this article the variable of interest is the marginal price instead of demand. This paper provides a graphical analysis by means of an easily reproducible automatization with the R project for statistical computing that allows to explore, visualize and understand the key variables that define its final value. Mibel 2011 and 2012 data are used for ilustrations. The results show the importance of the calendar effect, seasonality and trend as principal factors to take into account for posterior fases: modeling and forecasting.