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\footnotesize
\noindent Statistica Sinica {\bf 13}(2003), 409-422
\vspace{3pc} \normalsize
\centerline{\large\bf OBJECTIVE BAYESIAN INFERENCE FOR RATIOS OF}
\vspace{2pt}
\centerline{\large\bf REGRESSION COEFFICIENTS IN LINEAR MODELS}
\vspace{.25cm}
\centerline{Malay Ghosh, Ming Yin and Yeong-Hwa Kim}
\vspace{.4cm}
\centerline{\it University of Florida,
%Duke University and Samsung Corporation}
Analytical Sciences Incorporated
and Chung-Ang University}
\vspace{.55cm}
\begin{quotation}
\noindent {\it 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
Bay\-esian 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.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Calibration, Fieller-Creasy, matching priors, orthogonal transformation,
parallel-line assay, reference priors, slope-ratio assay.
\end{quotation}
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