A COMPARISON OF UNCERTAINTY CRITERIA FOR CALIBRATION

Calibration consists of using a fitted regression line to estimate the value of an unobserved independent variable x corresponding to an obs erved dependent variable y. To construct a confidence interval for a s ingle x, Eisenhart introduced a procedure that consists of inverting p rediction intervals around the regression line. Numerous other inferen ce procedures have been proposed for multiple-use calibration, in whic h a single fitted regression line is used repeatedly to estimate many x's. We provide a synthesis of this literature and offer some numerica l comparisons. We also attempt to motivate the use of various criteria based on the particular points of view of the various parties involve d in determining the calibration or using the results. In addition, we derive probability expressions for computing exact simultaneous predi ction intervals that enable the construction of tighter limits than ar e currently available based on that criterion.