Browsing by Subject "Bayes factors"

Now showing 1 - 3 of 3
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    A Bayesian joinpoint regression model with an unknown number of break-points
    (Institute of Mathematical Statistics, 2011-09) Martínez-Beneito, M.A.; García-Donato, G.; Salmerón, D.; Ciencias Sociosanitarias
    Joinpoint regression is used to determine the number of segments needed to adequately explain the relationship between two variables. This methodology can be widely applied to real problems, but we focus on epidemiological data, the main goal being to uncover changes in the mortality time trend of a specific disease under study. Traditionally, Joinpoint regression problems have paid little or no attention to the quantification of uncertainty in the estimation of the number of change-points. In this context, we found a satisfactory way to handle the problem in the Bayesian methodology. Nevertheless, this novel approach involves significant difficulties (both theoretical and practical) since it implicitly entails a model selection (or testing) problem. In this study we face these challenges through (i) a novel reparameterization of the model, (ii) a conscientious definition of the prior distributions used and (iii) an encompassing approach which allows the use of MCMC simulation-based techniques to derive the results. The resulting methodology is flexible enough to make it possible to consider mortality counts (for epidemiological applications) as Poisson variables. The methodology is applied to the study of annual breast cancer mortality during the period 1980–2007 in Castellón, a province in Spain.
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    Open Access
    Linear contrasts for the one way analysis of variance: a Bayesian approach
    (Elsevier, 2016-02) Cano, J. A.; Carazo, C.; Salmerón Martínez, Diego; Ciencias Sociosanitarias
    Linear contrasts between means for the one way analysis of variance are studied for the first time as objective model selection problems. For it, Bayes factors for intrinsic priors are used and classical and Bayesian measures of evidence are compared.
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    Open Access
    Objective Bayesian model selection approach to the two way analysis of variance
    (Springer, 2018-03) Cano, J. A.; Carazo, C.; Salmerón Martínez, Diego; Ciencias Sociosanitarias
    An objective Bayesian procedure for testing in the two way analysis of variance is proposed. In the classical methodology the main effects of the two factors and the interaction effect are formulated as linear contrasts between means of normal populations, and hypotheses of the existence of such effects are tested. In this paper, for the first time these hypotheses have been formulated as objective Bayesian model selection problems. Our development is under homoscedasticity and heteroscedasticity, providing exact solutions in both cases. Bayes factors are the key tool to choose between the models under comparison but for the usual default prior distributions they are not well defined. To avoid this difficulty Bayes factors for intrinsic priors are proposed and they are applied in this setting to test the existence of the main effects and the interaction effect. The method has been illustrated with an example and compared with the classical method. For this example, both approaches went in the same direction although the large P value for interaction (0.79) only prevents us against to reject the null, and the posterior probability of the null (0.95) was conclusive.