An analysis of a bayes inverse regression method of confidence intervals in linear calibration
Larry T. Frazier · Journal of Statistical Computation and Simulation · 1974
The model conisdered in this paper is that of simple linear regression . The problem is to make statistical inferences about an unknown value of x, say X, corresponding to an additional observed value of y. Hoadley (1970)showed that the Inverse estimator of X (Krutchkoff, 1967) is Bayes with respect to a particular informative prior. In addition. He obtained the 100 (1 - α) % shortest posterior interval when this particular informative prior is justifiable. In order to determine the worth of Hoadley's interval in practical applications when the distribution of the true value X is unknown (which is usually the case), Monte Carlo experiments were conducted. With the exception of the lower confidences, the confidence interval is found to be always valid for X within the experimental range when using the end-point design.