Objective Bayesian analysis for the combined calibration problem

Abstract

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The univariate calibration problem is investigated, where different instruments, methods or laboratories are used to obtain response variables and explanatory variables in a linear regression model. We develop the objective Bayesian analysis for this problem by proposing a first and second order matching prior and a reference prior. It is shown that the posterior is improper under the second order matching prior, while the reference priors satisfy a first order matching criterion. We also provide conditions for proper posterior distributions with general priors such as matching and reference priors. The simulation study reveals that the matching prior is more effective than Jeffreys’ prior and the reference priors in terms of the target coverage probabilities in a frequentist sense, and a real example is given to illustrate the results.