Tilburge University - Methodology and Statistics
Bayes factors have been proven to be very useful when testing statistical hypotheses with inequality (or order) constraints and/or equality constraints between the parameters of interest. Two useful properties of the Bayes factor are its intuitive interpretation as the relative evidence in the data between two hypotheses and the fact that it can straightforwardly be used for testing multiple hypotheses. The choice of the prior, which reflects one's knowledge about the unknown parameters before observing the data, has a substantial effect on the Bayes factor. For this reason the prior must be chosen with care. In this talk I discuss three different issues that may occur when specifying the prior when testing order constrained hypotheses. First, the resulting Bayes factor may ignore model complexity. Second, the resulting Bayes factor may not be invariant for linear transformations of the data. Third, the resulting Bayes factor may be information inconsistent. For this reason, a new default Bayes factor is proposed that avoids these issues.