A precision profile, the relationship between the concentration of a substance and its measured precision, is a convenient way of conveying the ability of an immunoassay to accurately measure the concentration of a substance in blood serum. A precision profile is characterized by the definition of precision. Historically, precision has been evaluated as the standard error of an estimator of the concentration in a sample conditional on the true concentration. In this paper, Bayesian predictive inference is used to develop a new measure of precision based on the accuracy with which an assay could infer the concentration in a hypothetical new sample. This leads to a natural procedure for evaluating a precision profile that avoids using approximations such as those inherent in traditional methods.