AbstractIn a long‐running longitudinal study using complex machinery to obtain measurements, it is sometimes necessary to replace the machine. This can result in lack of continuity in the measurements that can overwhelm any treatment effect or time trend. We propose a Bayesian procedure implemented using Markov chain Monte Carlo to calibrate the measurements on the old machine utilizing both person‐specific and population information. The goal is to convert the previous measurements to values that can be treated as though they were made on the new machine. This methodology is applied to a bone mineral density study where the first densitometer uses gadolinium as the energy source (Lunar DP‐3) and the second uses X‐rays (Hologic QDR‐1000W). Finally, simulation results are presented to show the superiority of the proposed method over existing methods of cross calibration. Copyright © 2004 John Wiley & Sons, Ltd.