Numerical quantification of the results from a measurement uncertainty computation is considered in terms of the inputs to that computation. The primary output is often an approximation to the PDF (probability density function) for the univariate or multivariate measurand (the quantity intended to be measured). All results of interest can be derived from this PDF. We consider uncertainty elicitation, propagation of distributions through a computational model, Bayes’ rule and its implementation and other numerical considerations, representation of the PDF for the measurand, and sensitivities of the numerical results with respect to the inputs to the computation. Speculations are made regarding future requirements in the area and relationships to problems in uncertainty quantification for scientific computing.