Browsing by Subject "Model selection"

Now showing 1 - 2 of 2
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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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    Bayesian model selection approach to the one way analysis of variance under homoscedasticity
    (Springer, 2013-06) Cano, J. A.; Carazo, C.; Salmerón Martínez, Diego; Ciencias Sociosanitarias
    An objective Bayesian model selection procedure is proposed for the one way analysis of variance under homoscedasticity. Bayes factors for the usual default prior distributions are not well defined and thus Bayes factors for intrinsic priors are used instead. The intrinsic priors depend on a training sample which is typically a unique random vector. However, for the homoscedastic ANOVA it is not the case. Nevertheless, we are able to illustrate that the Bayes factors for the intrinsic priors are not sensitive to the minimal training sample chosen; furthermore, we propose an alternative pooled prior that yields similar Bayes factors. To compute these Bayes factors Bayesian computing methods are required when the sample sizes of the involved populations are large. Finally, a one to one relationship—which we call the calibration curve—between the posterior probability of the null hypothesis and the classical value is found, thus allowing comparisons between these two measures of evidence. The behavior of the calibration curve as a function of the sample size is studied and conclusions relating both procedures are stated.