Bayesian variable selection based on test statistics. Basic ideas and selected topics

      Аннотация: Having the possibility to correctly select the covariates, which are to be included in the final model is a major challenge in statistics, especially in the regression framework. A crucial problem of existing Bayesian variable selection procedures is the specification of complicated prior model parameters that appear in the selection set. As a consequence, applications based on these methodologies are sometimes limited. The drivers of this book are the wish to reduce the subjectivity that is associated with the specification of prior distributions. Furthermore, since, in spite of everything, prior specifications are not completely eliminated, an analysis of how to choose them and an investigation of the involved effects in our Bayesian variable selection are proposed. To achieve these objectives, work was structured into three major parts. In the first part, an innovative procedure to calculate Bayes factors based on standard test statistics is proposed. The second part deals with a Bayesian variable selection methodology which is constructed from the previously calculated test-based Bayes factors. Finally, since prognostic models are of central importance in medicine, applications to two concrete examples are developed in this field. As an outcome of this book it can be said that...

Ключевые слова: Bayesian variable selection, test statistics, Bayes factor, likelihood ratio statistics, chi-squared statistic, hypothesis testing, Bartlett's and Jeffrey's paradox, dependent and uniform prior, Leonhard Held, Ashkan Nikeghbali