On the Application of the Bayesian Approach to Estimating the Coverage Interval of a Bounded Measurand

The problem of estimating the measurement uncertainty near the natural measurand limits is of significant interest to practicing metrologists and is far from being resolved. The article considers the Bayesian approach to constructing an asymmetric coverage interval and estimating measurement uncertainty in the case where the set of permissible values of the measured quantity is bounded. Of particular interest is the case when the measured value is located near the boundary of the set of its permissible values, since the constructed «traditional» symmetric interval corresponding to a coverage factor value of two (for a confidence level of 95 %) goes beyond the boundaries of this set and, as a consequence, do not provide the specified level of confidence probability. When implementing the Bayesian approach, an important starting point is the choice of a priori density distribution. Four options for choosing a prior probability density are considered, including an asymmetric distribution from the family of two-sided power distributions (TSP). Recommendations are given for their selection and application depending on the proximity of the a priori estimate of the lower limit of the measured value, as well as the measured value, to the upper limit of the range of permissible values, relative to the measurement uncertainty value. A specialized software has been developed to estimate the posterior density characteristics (expectation, mode and standard deviation) of measurand distributions and construct the shortest coverage interval, as well as to calculate the confidence level corresponding to the «traditional» coverage interval obtained using expanded uncertainty. The use of this software allows to obtain complete information about the measurement accuracy and to make an informed choice when presenting the measurement result. The results obtained may be of interest to practicing metrologists in the development and certification of measurement techniques, processing of experimental data and presentation of measurement results when characterizing standard samples, as well as specialists involved in the application of methods of probability theory and mathematical statistics in solving practical problems.