Bayes factors for testing equality and inequality constrained hypotheses on variances

Lay Summary
There are often reasons to expect certain relations between the variances of multiple populations. For example, in an educational study one might expect that the variance of students’ performances increases or decreases across grades. Alternatively, it might be expected that the variance is constant across grades. Such expectations can be formulated as equality and inequality constrained hypotheses on the variances of the students’ performances. In this dissertation we develop automatic (or default) Bayes factors for testing such hypotheses. The methods we propose are based on default priors that are specified in an automatic fashion using information from the sample data. Hence, there is no need for the user to manually specify priors under competing (in)equality constrained hypotheses, which is a difficult task in practice. All the user needs to provide is the data and the hypotheses. Our Bayes factors then indicate to what degree the hypotheses are supported by the data and, in particular, which hypothesis receives strongest support.