A Bayesian approach to evaluating uncertainty of inaccurate categorical measurements

•A Bayesian approach to treating sampled categorical measurement results is proposed.•Misclassification errors and prior population information are taken into account.•The appropriate estimators of population partition by categories are presented.•It is shown that Bayesian estimation may differ from the sampled one significantly.•A procedure involving new observed information for updating is proposed.

We show how to interpret sampled measurement results when they belong to a categorical scale. The proposed approach takes into account the sampled nature of observations and observation errors, and combines both with prior information (if exists) about the studied population. The appropriate mathematical tools are presented, considering all these aspects, and providing an adequate description of the partition of the studied property by categories and its parameters. We demonstrate that the most likely or expected estimators may differ significantly from those observed in the sample, and sometimes even conflict with the assumed confusion matrix. The technique of determining the conflict-free region is presented, as well as the two-stage procedure of assessment updating, based on the verification of the accordance of the new observed information to the already available one. The main propositions of the paper are supported by numerical examples and graphs.