Monte Carlo uncertainty calculations with small-sample estimates of complex quantities

摘要

Three statistical distributions have been tested as candidates to represent the uncertainty of complex-valued quantities in Monte Carlo measurement uncertainty calculations. Two candidates are Bayesian multivariate t-distributions with 'non-informative' priors. The other is the distribution of a 'generalized pivotal quantity' (GPQ) for a multivariate mean. The best performance observed was from the GPQ: the two multivariate t-distributions were unsatisfactory in terms of coverage. The testing methodology is general and can be used to check the validity of other uncertainty calculation procedures.