Person:
Gómez Villegas, Miguel Ángel

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First Name
Miguel Ángel
Last Name
Gómez Villegas
URI
https://hdl.handle.net/20.500.14352/75682
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Estadística e Investigación Operativa
Area
Estadística e Investigación Operativa
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2013 - 20142
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Now showing 1 - 2 of 2
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    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, Luis
    DNA 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.
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    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, Beatriz
    A 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.