Bayes Factors for One Sided Hypothesis Testing in Linear Calibration

This article considers one side hypothesis testing on the unknown value of the explanatory variable in the univariate linear calibration. The problem is formulated in a general form and the solution is suited for a large set of models, namely when the sampling distribution belongs to a particular class, defined in Gleser & Hwang (1987). We discuss the drawbacks of frequentist solutions and we show how a proper Bayesian analysis encounters relatively similar difficulties. We explore the performances of some noninformative Bayesian approaches to testing, namely default Bayes factors. Default Bayes factors based on Jeffreys' priors seem to provide sensible results although not all the problems seems to be solved.