A further look at the Bayesian approach to calibration

This paper reviews and investigates the linear calibration or inverse linear regression problem from the Bayesian viewpoint. A posterior distribution is obtained for the concomitant variable x f in the simple linear regression model given the n pairs (x i ,y i ) and y f . The resulting confidence region estimator is compared with two other Bayesian confidence region estimators previously obtained by Dunsmore (1968) and by Hoadley (1970). The assumptions and applicability of the three methods are also discussed. A simulation experiment is performed analyzing and comparing the posterior confidence interval developed in this paper and Hoadley's posterior interval.