Abstract: The paper considers the standard linear multiple regression model where the parameter of interest is a ratio of two regression coefficients. The general model includes the calibration model, the Fieller-Creasy problem, slope-ratio assays, parallel-line assays and bioequivalence. We provide a unified objective Bayesian analysis for such problems. Both reference priors and probability matching priors are found. Based on some numerical findings, our recommended prior is the one-at-a-time reference prior. The analysis is greatly facilitated by an orthogonal (Cox and Reid (1987)) reparameterization of the original parameter vector.
Key words and phrases: Calibration, Fieller-Creasy, matching priors, orthogonal transformation, parallel-line assay, reference priors, slope-ratio assay.