Comparison of Hypothesis Testing and Bayesian Model Selection |
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Authors: | Herbert Hoijtink Irene Klugkist |
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Affiliation: | (1) Department of Methodology and Statistics, University of Utrecht, P.O.Box 80140, 3508 TC Utrecht, The Netherlands |
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Abstract: | The main goal of both Bayesian model selection and classical hypotheses testing is to make inferences with respect to the
state of affairs in a population of interest. The main differences between both approaches are the explicit use of prior information
by Bayesians, and the explicit use of null distributions by the classicists. Formalization of prior information in prior distributions
is often difficult. In this paper two practical approaches (encompassing priors and training data) to specify prior distributions
will be presented. The computation of null distributions is relatively easy. However, as will be illustrated, a straightforward
interpretation of the resulting p-values is not always easy. Bayesian model selection can be used to compute posterior probabilities for each of a number of
competing models. This provides an alternative for the currently prevalent testing of hypotheses using p-values. Both approaches will be compared and illustrated using case studies. Each case study fits in the framework of the
normal linear model, that is, analysis of variance and multiple regression. |
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Keywords: | Bayesian model selection encompassing prior posterior model probability p-value training data |
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