A Bayesian Analysis of the Linear Calibration Problem

Abstract

As part of a Bayesian analysis of the linear calibration problem, a posterior distribution is derived that is mathematically identical to the structural distribution obtained by Kalotay (1971) but different from the Bayesian distribution obtained by Hoadley (1970). Useful approximations are given. Although this posterior distribution has infinite variance, no practical problems arise in using it. The controversy concerning infinite variances and the use of inverse regression is discussed.

KEY WORDS:

• Calibration
• Bayesian inference
• Regression
• Inverse regression
• Intervals of highest posterior density