The Cosine Error: A Bayesian Procedure for Treating a Non-repetitive Systematic Effect

An inconsistency with respect to variable transformations in our previous treatment of the cosine error example with repositioning (Metrologia, vol. 47, pp. R1–R14) is pointed out. The problem refers to the measurement of the vertical height of a column of liquid in a manometer. A systematic effect arises because of the possible deviation of the measurement axis from the vertical, which may be different each time the measurement is taken. A revised procedure for treating this problem is proposed; it consists in straightforward application of Bayesian statistics using a conditional reference prior with partial information. In most practical applications, the numerical differences between the two procedures will be negligible, so the interest of the revised one is mainly of conceptual nature. Nevertheless, similar measurement models may appear in other contexts, for example, in intercomparisons, so the present investigation may serve as a warning to analysts against applying the same methodology we used in our original approach to the present problem.